PhysicsPhysics QuestionsPhysics – Motion In A Plane Questions for CBSE Class 11th

Physics – Motion In A Plane Questions for CBSE Class 11th

  1. A body is thrown horizontally from the top of a tower of height 5 m. It touches the ground at a distance of 10 m from the foot of the tower. The initial velocity of the body is (Take, g = 10 ms -2 )
  2. A body is projected at an angle of 30 0 with the horizontal with momentum p . At its highest point, the magnitude of the momentum is
  3. A projectile is fired from ground level at an angle θ above the horizontal. The elevation angle ϕ of the highest point as seen from the launch point is related to θ by the relation
  4. A projectile is thrown with an initial velocity of ( a i ^ + b j ^ ) ms – 1 . If the range of the projectile is twice the maximum height reached by it, then
  5. The greatest height to which a man can throw a stone is h . The greatest distance to which he can throw it will be
  6. A ball is thrown up with a certain velocity at an angle θ to the horizontal. The kinetic energy KE of the ball varies with horizontal displacement x as
  7. A body of mass m is thrown upwards at an angle θ with the horizontal with velocity v . While rising up the velocity of the mass after t seconds will be
  8. If the instantaneous velocity of a particle projected as shown in figure is given by v = a i ^ + ( b – c t ) j ^ . where a , b and c are positive constants, the range on the horizontal plane will be
  9. A particle moves in the xy-plane with a constant acceleration g in the negative y-direction. Its equation of motion is y = ax – bx 2 , where a and b are constants. Which of the following are correct?
  10. A shell is fired with a horizontal velocity in the positive x-direction from the top of an 80m high cliff. The shell strikes the ground 1330 m from the base of the cliff. What is the initial speed of the shell? (Take g = 10 m/s 2 )
  11. A ball rolls off the top of a stair case with a horizontal velocity of 4.5 ms -1 . If the steps are 0.2 metre high and 0.3 metre broad and g = 10 ms -2 , then the ball will strike the nth step where n is equal to (g=10 m/s 2 )
  12. Which of the following statements is false regarding the vectors?
  13. A person moves 30 m north, then 30 m east, then 30 2 south-west. His displacement from the orginal position is
  14. 100 coplanar forces each equal to 10 N act on a body. Each force makes angle π 50 with the preceding force. What is the resultant of the forces?
  15. If A is a vector of magnitude 5 units due east. What is the magnitude and direction of a vector – 5 A ?
  16. Which one of the following statements is true?
  17. One of the rectangular components of velocity of 80 kmh – 1 is 40 Km h – 1 What are the other components ?
  18. A body is projected with velocity u such that its horizontal range and maximum vertical heights are same. The maximum heights is
  19. The height y and horizontal distance x covered by a projectile in a time t seconds are given by the equations y = 8t – 5t 2 and x = 6t. If x and y are measured in metres, the velocity of projection is
  20. If the maximum vertical height and horizontal ranges of a projectile are same, the angle of projection will be
  21. A person throws a bottle into a dustbin at the same height as he is 2m away at an angle of 45 0 . The velocity of projection is
  22. A stone is projected horizontally with a velocity 9.8 ms –1 from a tower of height 100 m. Its velocity one second after projection is
  23. In the locus diagrams of two projectiles I and 2 as shown in the fig.,
  24. A car 2 m long and 3m wide is moving at 10 m/s when a bullet hits it in a direction making an angle of tan – 1 ( 3 4 ) with the car as seen from the ground. The bullet enters one edge of the car at the corner and passes out at diagonally opposite corner. Neglecting gravity, the time for the bullet to cross the car is
  25. A particle is moving on a circular path of radius r with uniform speed v. What is the displacement of the particle after it has described an angle of 60 0 ‘?
  26. Two particles move in a uniform gravitational field with an acceleration g. At the initial moment the particles were located at one point and move with velocities v 1 = 3.0 m/s and v 2 = 4.0 m/s horizontally in opposite directions. Find the distance between the particles at the moment when their velocity vectors become mutually perpendicular.
  27. In 1.0 s, a particle goes from point A to point B, moving in a semicircle of radius 1.0 m (see figure). The magnitude of the average velocity is
  28. Time taken by the projectile to reach from I to.B is t. Then the distance AB is equal to:
  29. A particle is projected from the inclined plane at angle 37 0 with the inclined plane in upward direction with speed l0 m/s. The angle of inclined plane with horizontal is 53 o . Then the maximum height attained by the particle from the inclined plane will be –
  30. A body of mass m is projected horizontally with a velocity v from the top of a tower of height h and it reaches the ground at a distance x from the foot of the tower. If a second body of mass 2m is projected horizontally from the top of a tower of height 2h, it reaches the ground at a distance 2x from the foot of the tower. The horizontal velocity of the second body is:
  31. From the top of a tower of height 40 m, a ball is projected upwards with a speed of 20 ms – l at an angle of elevation of 30 o . Then the ratio of the total time taken by the ball to hit the ground to the time taken to ball come at same level as top of tower.
  32. A body of mass m thrown horizontally with velocity v, from the top of tower of height h touches the level ground at a distance of 250 m from the foot of the tower. A body of mass 2 m thrown horizontally with velocity v 2 , from the top of tower of height 4h will touch the level ground at a distance x from the foot of tower. The value of x is
  33. A body is projected from ground with a speed of 40 m/s making an angle of 30 o with horizontal. The body crosses a horizontal line twice in a time interval Δ t . If the height of the line above the ground is 15 m, find Δ t . [Take g = 10 m/s 2 ]
  34. A particle is moving in xy plane and equation of its trajectory is y = 120 x − 3 x 2 where x and y are in metre. When the distance of the particle from x-axis is maximum, speed of the particle is
  35. A body is projected from ground with a velocity ‘u’ making an angle of 60 o with horizontal. If the body just clears the building in a time interval of 2 sec, maximum height attained by the body is
  36. Which of the following is the graph between the height (h) of a projectile and time (t), when it is projected from the ground?
  37. Two projectiles A and B are thrown from the same point with velocities v and v /2, respectively. If B is thrown at an angle 45° with horizontal, what is the inclination of A when their ranges are the same?
  38. The velocity at the maximum height of a projectile is half of its initial velocity of projection ( μ ). Its range on horizontal plane is
  39. A ball is thrown from the ground to a wall 3 m high at a distance of 6 m . If the ball just clears the wall and falls 18 m away from the wall, the angle of projection of ball is
  40. At the height 80 m, an aeroplane is moving with 150 m s – 1 . A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped? (Take, g = 10 m s – 2 )
  41. An object is thrown towards the tower which is at a horizontal distance of 50 m with an initial velocity of 10 ms -1 and making an angle 30° with the horizontal. The object hits the tower at certain height. The height from the bottom of the tower, where the object hits the tower is (Take, g = 10 ms -2 )
  42. A particle is projected with a velocity v , so that its horizontal range twice the greatest height attained. The horizontal range is
  43. A body is projected from the ground with a velocity v = ( 3 i ^ + 10 j ^ ) ms – 1 . The maximum height attained and the range of the body respectively are (Take, 9 = 10 ms -2 )
  44. Two balls are thrown simultaneously from ground with same velocity of 10 ms -1 but different angles of projection with horizontal. Both balls fall at same distance 5 3 m from point of projection. What is the time interval between balls striking the ground?
  45. A bomber flying with a horizontal velocity of 500 km/h at an altitude of 5 km wants to hit a train moving with a constant velocity of 100 km/h in the same direction and in the same vertical plane. The angle θ between the line of sight of the target and the horizontal at the instant the bomb should be released is
  46. Which of the graph is between the height (h) of a projectile and time (t)
  47. The range R of projectile is same when its maximum heights are h 1 and h 2 . What is the relation between R and h 1 & h 2 ?
  48. The path followed by a body projected along y-axis is given as by y = 3 x − ( 1 / 2 ) x 2 , if g = 10 m / s 2 , then the initial velocity of projectile is (x and y are in m).
  49. A projectile is projected with initial velocity 6   i ^ + 8 j ^ m / s . If g = 10 m/s 2 , then what is the horizontal range of the projectile?
  50. The path followed by a body projected along y-axis is given as by y = 3 x − 1 / 2 x 2 , if g = 10 m/s 2 , then the initial velocity of projectile is (x and y are in m)
  51. A projectile is projected with initial velocity ( 6 i ^ + 8 j ^ ) m / s . If g = 10 m / s 2 , then what is the horizontal range of the projectile?
  52. A block slides off a horizontal table 1 m high with a speed of 3 m/s. Find the horizontal distance from the edge of the table at which the block strikes the floor: (Take g = 9.8 m/s 2 ).
  53. Person A is standing on the top of a building of height 25 m he wants to throw his gun to person B who stands on top of another building of height 20 m at distance 15 m from first building. The horizontal speed for which it possible is (g=10 m/s 2 )
  54. A stone is projected horizontally with a velocity of 40 m/s from a tower. Velocity of the body after 4 sec is (g=10 m/s 2 )
  55. A particle is projected at an angle of 600 above the horizontal with a speed of 10 m/s. After some time the direction of its velocity makes an angle of 30° above the horizontal. The speed of the particle at this instant is
  56. From the top of tower of height 20 m, two bodies are simultaneosuly projected one due north and other due west with equal speeds each of 10 m/s. Find the distance between them when they reach ground g =10 m / s 2
  57. The time taken by a particle to slide down a smooth inclined plane is double the time it would take in falling down through a height equal to the vertical height of the plane. The inclination of the plane with horizontal is:
  58. What is the angle between P and the resultant of ( P + Q ) and ( P − Q ) ?
  59. There are two forces vectors, one of 5 N and other of 12 N. At what angle the two vectors be added to get resultant vector of 17 N, 7 N and 13 N respectively?
  60. Which pair of the following forces will never give resultant force of 2 N?
  61. A force of 6 kg and another of 8 kg can be applied together to produce the effect of a single force of
  62. A unit vector in the direction of resultant vector of A   =   − 2 i ^ + 3 j ^ + k ^     and    B   =   i ^ + 2 j ^ − 4 k ^    is
  63. A particle moves towards east with velocity 5 m/s. After 10 seconds its direction changes towards north with same velocity. The average acceleration of the particle is
  64. If the resultant of two forces of magnitude p and 2p is perpendicular to p, then the angle between the forces is
  65. A particle moves in such a way that its position vector varies with time as r   =   Acosωt i ^ + Asinωt j ^ . The initial velocity of the particle is
  66. What are the maximum number of rectangular components of a vector which can be split in space and in plane respectively
  67. Let the angle between two nonzero vectors and be 120 0 and its resultant be .
  68. The minimum number of non coplanar forces that can keep a particle in equilibrium is
  69. I f A and B persons are moving with V A and V B velocities in opposite directions. Magnitude of relative velocity of B w.r.t. A is x and magnitude of relative velocity of A w.r.t B is y. Then
  70. For body thrown horizontally from the top of a tower,
  71. A stone is just dropped from the window of a train moving along a horizontal straight track with uniform speed. The path of the stone is
  72. A body is in pure rotation. The linear speed ν of the particle, the distance r of the particle from the axis and the angular velocity ω of the body are related as ω = V/r . Thus
  73. To go from town A to town B a plane must fly about 1780 km at an angle of 30 o West of North. How far north of A is B ?
  74. Two vectors a and b have equal magnitudes of 12 units. These vectors are making angles 30 o and 120 o with the x axis respectively. Their sum is r . Find the x and y components of r .
  75. If its components in yz plane and zx plane are respectively
  76. In a projectile motion the velocity a) is always perpendicular to the acceleration b) is not always perpendicular to the acceleration c) is perpendicular to the acceleration for one instant only d) is perpendicular to the acceleration for two instants.
  77. A particle moves along a horizontal circle with constant speed. If ‘a’ is its acceleration and ‘E’ is its kinetic energy A) a is constant B) E is constant C) a is variable D) E is variable
  78. A vector rotates about its tail through an angle 37 o in anticlockwise direction then the new vector is
  79. The resultant of two equal forces is 141.4 N when they are mutually perpendicular. When they are inclined at an angle 120º, then the resultant force will be
  80. Two bodies are projected at angles 30 0 and 60 0 to the horizontal from the ground such that the maximum heights reached by them are equal. Then a) Their times of flight are equal b) Their horizontal ranges are equal c) The ratio of their initial speeds of projection is √3 :1 d) Both take same time to reach the maximum height. Mark the correct answer as
  81. The resultant of two forces 2P and is . The angle between the forces is
  82. If and , then R 2 + S 2 is equal to
  83. The greatest and least resultant of two forces are 7 N and 3 N respectively. If each of the force is increased by 3 N and applied at 60°. The magnitude of the new resultant is
  84. Two forces are such that the sum of their magnitudes is 18 N, the resultant is when they are at 120 o . Then the magnitude of the forces are
  85. Figure shows three vectors , and , where R is the midpoint of PQ. Then which of the following relations is correct?
  86. A particle has an initial velocity 3 i ^ + 4 j ^ and an acceleration of 0 . 4 i ^ + 0 . 3 j ^ . Its speed after 10 sec is
  87. Keeping the velocity of projection constant, the angle of projection is increased from 0° to 90º. Then the maximum height of the projectile
  88. A body is projected with velocity 24 ms –1 making an angle 30° with the horizontal. The vertical component of its velocity after 2 s is (g = 10 ms –2 )
  89. A body projected at 45° with a velocity of 20 m/s has 10 m decrease in range due to air resistance. Then the final range is (g = 10ms -2 )
  90. The rectangular components of a vector lying in xy plane are (n+1) and 1. If coordinate system is turned by 60 o , they are n & 3 respectively the value of ‘n’
  91. It is possible to project a particle with a given speed in two possible ways so that it has the same horizontal range ‘R’. The product of time taken by it in the two possible ways is
  92. A body is projected horizontally from a height of 78.4 m with a velocity 10 ms -1 . Its velocity after 3 seconds is? [g = 10 ms -2 ] (Take direction of projection on i ^ and vertically upward direction on j ^ ).
  93. A body is projected horizontally from the top of a tower. When the body strikes the ground, its velocity is V and the direction of motion makes 30 0 with the horizontal. The velocity of projection is
  94. Time of flight of a projectile is 8 sec. If g = 10 m / s 2 , vertical component of velocity of projection is
  95. The path of a projectile in the absence of air drag is shown in the figure by dotted line. If the air resistance is not ignored then which one of the paths shown in the figure is appropriate for the projectile?
  96. A plane surface is inclined making an angle β above the horizon. A bullet is fired with the point of projection at the bottom of the inclined plane with a velocity u; then the maximum range is given by:
  97. The velocity of a projectile at the initial point A is ( 2 i ⏞ + 3 j ⏞ ) m/s. Its velocity (in m/s) at point B is
  98. The angle which the velocity vector of a projectile thrown with a velocity u at an angle θ to the horizontal will make with the horizontal after time t of its being thrown up is
  99. A projectile A is projected from ground. An observer B running on ground with uniform velocity of magnitude ‘v’ obseryes A to move along a straight line. The time of flight of A as measured by B is T. Then the range R of projectile on ground is
  100. The magnitude of displacement of a particle moving in a circle of radius a with constant angular speed ω varies with time t is
  101. A car speeds up in a circular path. Which of the following figures illustrates the acceleration of the car?
  102. A particle P is moving in a circle of radius ‘a’ with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio
  103. A ball thrown down the incline strikes at a point on the incline 25 m below the horizontal as shown in the figure. If the ball rises to a maximum height of 20 m above the point of projection, the angle of projection a (with horizontal x axis) is
  104. A fighter plane is flying horizontally at an altitude of 1.5 km with speed 720 km h – 1 . At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target? (Take g = 10 ms – 2 )
  105. A boy projects a stone vertically perpendicular to the trolley car with a speed v. If the trolley car moves with a constant velocity u, the horizontal range of the stone is:
  106. A boy projects a stone vertically perpendicular to the trolley car with a speed v. If the trolley car moves with a constant velocity u, the horizontal range of the stone is:
  107. A boy projects a stone vertically perpendicular to the trolley car with a speed v. If the trolley car moves with a constant velocity u, the time of flight of the stone is:
  108. A ball is projected with a velocity 3 i ^ + 4 j ^ m/s . The time after which its velocity vector is normal to initial velocity vector is (g = 10 m/ s 2 )
  109. A particle is projected under gravity with velocity 2 ag from a point at a height h above the level plane at an angle θ to it. The maximum range R on the ground is:
  110. A ball is thrown from the top of a tower with an initial velocity of 10 ms – 1 at an angle of 30 o with the horizontal. If it hits the ground at a distance of 17.3 m from the back of the tower, the height of the tower is (Take g: 10 ms – 2 )
  111. Two tall buildings are 30 m apart. The speed with which a ball must be thrown horizontally from a window 150 m above the ground in one building so that it enters a window 27.5 m from the ground in the other building is:
  112. The ceiling of a hall is 40 m high. For maximum horizontal distance, the angle at which the ball may be thrown with a speed of 56 ms – 1 without hitting the ceiling of the hall is
  113. A body is projected at 60 o with ground. It covers a horizontal distance of 100 m. If the same body is projected at 60 0 with vertical with same velocity, the new range is
  114. The speed of a projectile at its maximum height is 3 2 times its initial speed. If the range of the projectile is n times the maximum height attained by it, n is equal to:
  115. A stone is thrown at an angle θ to the horizontal reaches a maximum height H. Then the time of flight of stone will be:
  116. The equation of motion of a projectile is : y = 12x- 3 4 x 2 The horizontal component of velocity is 3 ms – 1 . Given that g = 10 ms – 2 , what is the range of the projectile?
  117. A person can throw a stone to a maximum distance of h metre. The greatest height to which he can throw the stone is:
  118. A particle is projected with a velocity u making an angle θ with the horizontal. At any instant its velocity becomes v which is perpendicular to the initial velocity u. Then v is
  119. The point from where a ball is projected is taken as the origin of the coordinate axes. The x and y components of its displacement are given by x = 6t and y = 8t – 5 t 2 . What is the velocity of projection?
  120. A body is projected from ground in uniform gravitational field making an angle with horizontal. If ratio of its maximum potential energy to the minimum kinetic energy is 3, the angle of projection is
  121. Choose the correct relation from the following for any motion in space
  122. A projectile is thrown at an angle θ with the horizontal and its range is R 1. It is then thrown at an angle θ with vertical and the range is R 2, then
  123. Which of the following is the altitude-time graph for a projectile thrown horizontally from the top of the tower?
  124. The horizontal range of a projectile fired at an angle of 15 0 is 50 m. If it is fired with the same speed at an angle of 45°, its range will be
  125. Two stones having different masses m 1 and m 2 are projected at an angle α and (90° – α ) with same speed from same point. The ratio of their maximum heights is
  126. A particle moves in the XY -plane according to the law x = k t , y = k t ( 1 – α t ) , where k and α are positive constants and t is time. The trajectory of the particle is
  127. The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection The percentage increase in the horizontal range will be
  128. Four bodies P , Q , R and S are projected with equal velocities having angles of projection 15°, 30°, 45° and 60° with the horizontal respectively. The body having shortest range is
  129. A stone is thrown at an angle θ with the horizontal, reaches a maximum height H. Then, the time of flight of stone will be
  130. The equation of motion of a projectile is y = 12 x – 3 4 x 2 What is the range of the projectile?
  131. A ball of mass m is projected from the ground with an initial velocity u making an angle of θ with the vertical. What is the change in velocity between the point of projection and the highest point?
  132. A ball is thrown up with a certain velocity at an angle θ to the horizontal. The kinetic energy KE of the ball varies with height h as
  133. The equation of projectile is Y = 3 X – 1 2 g X 2 The velocity of projection is
  134. A ball is thrown from a point O aiming a target at angle 30 0 with the horizontal, so that the ball hits the target at B but the ball hits at point A , a vertical distance h below B . If the initial velocity of the ball is 20 m s – 1 and the horizontal distance between O and C is 10m. Find the value of h.
  135. A ball is thrown from a point with a speed ν 0 at an angle of projection θ . From the same point and at the same instant, a person starts running with a constant speed ν 0 / 2 to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?
  136. A ball rolls off the edge of a horizontal table top 4 m high. If it strikes the floor at a point 5 m horizontally away from the edge of the table, what was its speed at the instant it left the table?
  137. The horizontal range and maximum height attained by a projectile are R and H, respectively. If a constant horizontal acceleration a = g/4 is imparted to the projectile due to wind, then its horizontal range and maximum height will be
  138. A projectile is fired at an angle of 30 0 to the horizontal such that the vertical component of its initial velocity is 80 m s – 1 . Its time of flight is T. Its velocity at t = T/4 has a magnitude of nearly
  139. Balls A and B are thrown from two points lying on the same horizontal plane separated by a distance 120 m. Which of the following is true?
  140. I. Particle-1 is dropped from a tower and particle-2 is projected horizontal from the same tower, then both the particles reach the ground simultaneously. II. Both the particles strike the ground with different speeds. Which of the following statement{s) is/are correct?
  141. An arrow is shot into air. Its range is 200 m and its time of flight is 5 s. If g = 10 ms -2 , then horizontal component of velocity and the maximum height will be respectively
  142. From an inclined plane two particles are projected with same speed at same angle θ, one up and the other down the plane as shown in fig. (3). Which statement(s) is/are correct?
  143. A particle (1) is projected with speed V from a point O making an angle of 30 o with the vertical. At the same instant, a second particle (2) is thrown vertically upwards with velocity v from a point A. The two particles reach H, the highest point on the parabolic path of particle (1) simultaneously. The ratio of V/v is
  144. A projectile is given an initial velocity of 5 m/s at an angle 30° below horizontal from the top of a building 25 m high. Find (a) the time after which it hits the ground; (b) the distance from the building where it strikes the ground. (g = 10 m/s 2 )
  145. A block slides off a horizontal table 1 m high with a speed of 3 m/s. Find the horizontal distance from the edge of the table at which the block strikes the floor: (Take g = 9.8 m/s 2 ).
  146. A particle is projected with a speed v o at an angle θ above the horizontal surface such that the ratio of the kinetic energy at the highest point and the point of projection is 3:4. The change in velocity of the particle between these two points is
  147. Five balls A,B,C,D and E are projected with the same speed making angles of 10 o , 30 o , 45 o , 60 o and 80 o respectively with the horizontal. Which ball will strike the ground at the farthest point?
  148. The path of one projectile as seen by an observer on another projectile is a/an :
  149. A particle is projected with a velocity , so that its range on a horizontal plane is twice the greatest height attained. If g is acceleration due to gravity, then its range is
  150. Two paper screens A and B are separated by 150 m. A bullet pierces A and then B. The hole in B is 15 cm below the hole on screen A. If the bullet is travelling horizontally at the time of hitting A, then the velocity of the bullet at A is : (Take g = 10 ms -2 )
  151. A body is projected at such angle that the horizontal range is three times the greatest height. The angle of projection is :
  152. Two tall buildings are 30 m apart. The speed with which a ball must be thrown horizontally from a window 150 m above the ground in one building so that it enters a window 27.5 m from the ground in the other building is
  153. A projectile is projected with initial velocity ( 6 i ^ + 8 j ^ ) m / sec .If g = 10 ms − 2 , then horizontal range is
  154. A body projected at an angle with the horizontal has a range 300 m. If the time of flight is 6 s, then the horizontal component of velocity is
  155. Which of the following is the altitude-time graph for a projectile thrown horizontally from the top of the tower ?
  156. An aluminium ball ‘A’ and an iron ball ‘B’ of same volume are thrown horizontally with the same velocity from the top of a tower of certain height. Neglecting air resistance, then
  157. A ball is projected horizontally from the top of a building 19.6 m high. If the line joining the point of projection to the point where it hits the ground makes an angle of 45° to the horizontal, the initial velocity of the ball is
  158. A body is projected with a velocity of (3i + 4j + 5k) m/s from the ground. Taking XY-plane as ground and Z axis as vertical, its range is (g = 10 m/s 2 )
  159. A body is thrown at some angle from the ground. The magnitude of change in velocity of body in 5 s, if it is still in air, is [g = 10 m/s 2 ]
  160. A particle is projected at an angle of 60 0 above the horizontal with a speed of 10 m/s. After some time the direction of its velocity makes an angle of 30° above the horizontal. The speed of the particle at this instant is
  161. A cricketer of height 2.5 m throws a ball at an angle 30º with the horizontal such that it is received by another cricketer of same height standing at a distance of 50 m from the first one. The maximum height attained by the ball from the ground is
  162. An enemy plane is flying horizontally at an altitude of 2 km with a speed of 300 ms -1 . An armyman with an anti – aircraft gun on the ground sights the enemy plane when it is directly overhead and fires a shell with a muzzle speed of 600 ms -1 . At what angle with the vertical should the gun be fired so as to hit the plane ?
  163. Two bodies are thrown up, one at 45° and the other at 60°, to the horizontal. If both bodies attain the same vertical height, then the ratio of projected speed of the first projectile to that of the second projectile is
  164. The equation of trajectory of a particle is given by the equation y = ax + bx 2 where a & b are constants. Horizontal range is
  165. A gun fires a bullet at a speed of 140m / s. If the bullet is to hit a target at the same level as the gun and at 1km distance, the angle projection
  166. Person A is standing on the top of a building of height 25 m he wants to throw his gun to person B who stands on top of another building of height 20 m at distance 15 m from first building. The horizontal speed for which it possible is (g=10 m/s 2 )
  167. A body is thrown horizontally with a velocity of v m/s from the top of a tower of height 2h reaches the ground in ‘t’ seconds. If another body double the mass is thrown horizontally with a velocity 5v from the top of another tower of height 8h it reaches the ground in a time of
  168. A person throws a stone with a velocity 10 m/s at an angle tan ⁡ θ = 3 / 4 to horizontal from a point at distance 8 m from the wall. The stone just passes over the wall. The height of the wall is [g = 10m/ s 2 ]
  169. A projectile is thrown into space so as to have the maximum possible horizontal range equal to 400 m, taking the point of projection as the origin, the coordinates of the point where the velocity of the projectile is minimum, are
  170. A particle is projected horizontally from the top of the tower. The trajectory is
  171. The vectors A and B are such that lA+Bl=lA-Bl then the angle between the two vectors will be
  172. From the top of a tower of height h, a body is projected horizontally with velocity U on reaching the ground, the magnitude of change in velocity
  173. A particle is projected horizontally from the top of the tower. The trajectory is
  174. From the top of a tower of height h, a body is projected horizontally with velocity U on reaching the ground, the magnitude of change in velocity
  175. The horizontal range of a projectile is 4 3 times its maximum height. Its angle of projection will be:
  176. A ball is projected horizontally from the top of a building 19.6 m high. If the line joining the point of projection to the point where it hits the ground makes an angle of 45° to the horizontal, the initial velocity of the ball is
  177. The co-ordinates of a moving particle at any time t are given by x = αt 3 and y = βt 3 . The speed of the particle at time t is given by :
  178. A person throws a stone with a velocity 10 m/s at an angle tan ⁡ θ = 3 / 4 to horizontal from a point at distance 8 m from the wall. The stone just passes over the wall. The height of the wall is [g = 10m/ s 2 ]
  179. An aluminium ball ‘A’ and an iron ball ‘B’ of same volume are thrown horizontally with the same velocity from the top of a tower of certain height. Neglecting air resistance, then
  180. Oblique projectile motion consists of
  181. A body is thrown horizontally with a velocity of v m/s from the top of a tower of height 2h reaches the ground in ‘t’ seconds. If another body double the mass is thrown horizontally with a velocity 5v from the top of another tower of height 8h it reaches the ground in a time of
  182. A projectile is thrown into space so as to have the maximum possible horizontal range equal to 400 m, taking the point of projection as the origin, the coordinates of the point where the velocity of the projectile is minimum, are
  183. A gun fires a bullet at a speed of 140m / s. If the bullet is to hit a target at the same level as the gun and at 1km distance, the angle projection
  184. For a projectile the ratio of maximum height reached to the square of flight time is g = 10 ms − 2 .
  185. A cricketer of height 2.5 m throws a ball at an angle 30º with the horizontal such that it is received by another cricketer of same height standing at a distance of 50 m from the first one.The maximum height attained by the ball from the ground is
  186. A body is projected horizontally from the top of a tower. When the body strikes the ground, its velocity is V and the direction of motion makes 30 0 with the horizontal. The velocity of projection is
  187. A car runs at a constant speed on a circular track of radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is
  188. A ship A is moving Westwards with a speed of 10 kmh – 1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h – 1 . The time after which the distance between them becomes shortest, is
  189. A truck travelling due north at 20 m s – 1 turns west and travels with same speed. What is the change in velocity?
  190. The x and y coordinates of the particle at any time are x = 5t – 2 t 2 and y = 10t respectively, where x and y are in metres and t in seconds. The acceleration of the particle at t = 2 is
  191. A projectile is thrown with velocity U = 20 m/s ± 5% at an angle 600. If the projectile falls back on the ground at the same level then which of the following can not be a possible answer for range ?
  192. Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 m apart and of same height of 200 m, with the same velocity of 25 m/s. When and where will the two bullets collide? (g = 10 m / s 2 )
  193. A body is projected at an angle 60 0 with the horizontal and it just crosses a wall of height 3 m and hits the ground 2m behind the wall. Then the distance of the wall from the point of projection is
  194. Five equal forces of 10 N each are applied at one point and all are lying in one plane. If the angles between them are equal, the resultant force will be
  195. A    =    2 i ^ + j ^ ,    B   =   3 j ^ − k ^     and    C    =    6 i ^ − 2 k ^ .    Value   of    A − 2 B + 3 C would be
  196. The maximum and minimum magnitude of the resultant of two given vectors are 17 units and 7 unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is
  197. Force F 1 and F 2 act on a point mass in two mutually perpendicular directions. The resultant force on the point mass will be
  198. Two equal forces (P each) act at a point inclined to each other at an angle of 120 0 . The magnitude of their resultant is
  199. A particle is simultaneously acted by two forces equal to 4 N and 3 N. The net force on the particle is
  200. If A =   4 i ^ − 3 j ^ and B =   6 i ^ + 8 j ^ then magnitude and direction of A + B from +x axis will be
  201. Two vectors A and B inclined at an angle θ have a resultant R which makes an angle α with A   . If the direction of A   and B are interchanged, the resultant will have the same
  202. When two vectors of magnitudes P and Q are inclined at an angle θ , the magnitude of their resultant 2P. When the inclination is changed to 180- θ , the magnitude of the resultant is halved. Find the ratio of P to Q.
  203. Two forces of magnitudes P and Q are inclined at an angle ( θ ) the magnitude of their resultant is 3Q. When the inclination is changed to (180- θ ) the magnitude of the resultant force between Q. The ratio of the forces ( P Q ) is
  204. A balloon starts rising from the surface of earth. The ascent rate is constant and equal to v 0 . Due to wind the balloon gathers the horizontal velocity component v x = Ay. While A is constant and if y is the height of ascent, the horizontal drift of the balloon is:
  205. If two vector A    =    2 i ^ + 3 j ^ − k ^      and    − 4 i ^ − 6 j ^ − λ k ^ are parallel to each other then value of λ
  206. At which angle must the two forces (x+y) and (x-y) act so that the resultant may be x 2 + y 2
  207. A body is projected from ground with a velocity u = 40 i ^ + 30 j ^ m / s .     T h e n    i t s    r a n g e    i s    T a k e   g = 10   m / s 2
  208. Consider east as positive x-axis, north as positive y-axis and vertically upward direction as z-axis. A helicopter first rises up to an altitude of 100 m than flies straight in north 500 m and then suddenly takes a turn towards east and travels 1000 m east. What is position vector of helicopter?(Take starting point as origin)
  209. In x-y plane, a force 10 N acts at an angle 30 0 to the positive direction of x axis. The force can be written as
  210. A projectile is projected at an angle of 45° to the horizontal. The slope of trajectory of the body varies with time t as
  211. A particle has initial velocity ( 2 i ^ + 3 j ^ ) and acceleration ( 0 .3 i ^ + 0 .2 j ^ ) . The magnitude of velocity after 10 seconds will be
  212. If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:
  213. How many minimum number of coplanar vectors having different magnitudes can be added to give zero resultant?
  214. The magnitude of vectors A   ,    B    and    C are 3, 4 and 5 units respectively. If A + B = C , the angle between A a n d B is
  215. The velocity of a projectile at the initial point A is ( ( 2 i ^   + 3 j ^ ) m/s. Its velocity (in m/s) at point B is
  216. The maximum number of components a vector can be split are ?
  217. Which of the following statements is false regarding the vectors?
  218. If angle between A and B is π/3 , then angle between 2 A and -3 B is
  219. (Diagram) Figure shows the orientation of two vectors u and v in the XY plane If u = a i ^ + b j ^ and v = p i ^ + q j ^ which of the following is correct ?
  220. If = + then
  221. It is found that | + | = | | . This necessarily implies.
  223. Galileo writes that for angles of projection of a projectile at angles (45 0 + θ) and (45 0 – θ) , the horizontal ranges described by the projectile are in the ratio of (if θ ≤ 45 0 )
  224. Keeping the velocity of projection constant, the angle of projection is increased from 0 0 to 90 0 . Then the horizontal range of the projectile
  225. If a body is projected with an angle θ to the horizontal, then
  226. The acceleration of a projectile relative to another projectile is
  227. Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit the ground first ?
  228. A number of bullets are fired horizontally with different velocities from the top of a tower. They reach the ground
  229. A car makes a displacement of 100 m towards east and then 200 m towards north. Find the magnitude and direction of the resultant displacement.
  230. If and ,calculate the direction of
  231. One of the rectangular components of velocity of 20 ms –1 is 10 ms –1 . Find the other component.
  232. The direction cosines of a vector of magnitude 5√2 are , and then the vector is
  233. Which of the following is a null vector a) velocity vector of a body moving in a circle with a uniform speed b) velocity vector of a body moving in a straight line with a uniform speed c) position vector of the origin of the rectangular coordinate system d) displacement vector of a stationary object
  234. A bomber flying horizontally with constant speed releases a bomb from an aeroplane. a) The path of bomb as seen by the observer on the ground is parabola b) The path of the bomb as seen by a pilot is a straight line. c) The path of the aeroplane with respect to bomb is a straight line d) The path of the bomb as seen by pilot observed as parabola.
  235. A body is projected with an initial speed of 100√3 ms -1 at an angle of 60 0 above the horizontal. If g = 10ms -2 then velocity of the projectile a) Is perpendicular to its acceleration at the instant t = 15 sec. b) Is perpendicular to initial velocity of projection at t = 20 sec. c) Is minimum at the highest point d) Changes both in magnitude and direction, during its flight. Mark the answer as
  236. Two particles are projected from the same point with the same speed at different angles θ 1 and θ 2 to the horizontal. If their respective times of flights are T 1 and T 2 and horizontal ranges are same then a) θ 1 +θ 2 = 90 0 b) T 1 = T 2 tan θ 1 c) T 1 = T 2 tan θ 2 d) T 1 sin θ 2 = T 2 sin θ 1
  237. Set the following vectors in the increasing order of their magnitude a ) b) c)
  238. Maximum and minimum magnitudes of the resultant of two vectors of magnitudes P and Q are found to be in the ratio 3 : 1. Which of the following relations is true ?
  239. Which of the following sets of forces acting simultaneously on a particle keep it in equilibrium?
  240. Eleven forces each equal to 5 N act on a particle simultaneously. If each force makes an angle 30º with the next one, the resultant of all forces is
  241. If the sum of two unit vectors is also a vector of unit magnitude, the magnitude of the difference of the two unit vectors is
  242. If and the final velocity is and it is covered in a time of 10 sec, find the average acceleration vector.
  243. Resultant of two vectors of magnitudes P and Q is of magnitude ‘Q’. If the magnitude of is doubled now the angle made by new resultant with is
  244. The square of the resultant of two forces 4 N and 3 N exceeds the square of the resultant of the two forces by 12, when they are mutually perpendicular. The angle between the vectors is
  245. The magnitudes of two vectors and differ by 1. The magnitude of their resultant makes an angle of tan –1 (3/4) with P. The angle between P and Q is
  246. The resultant of two vectors and is .If the magnitude of is doubled, the new resultant becomes perpendicular to ,then the magnitude of is
  247. A Ship ‘A’ streams due north at a speed of 8 kmph and ship B due west at a speed of 6 kmph. The velocity of A w.r.t. B is.
  248. A man is travelling at 10.8 kmph in a topless car on a rainy day. He holds an umbrella at an angle of 37 0 with the vertical so that he does not wet. If rain drops falls vertically downwards, what is the velocity of rain ?
  249. The resultant of two forces F 1 and F 2 is F. If F 2 is reversed then the magnitude of resultant is 2F. If F 2 is doubled then the resultant is also doubled. Find the ratio F 1 : F 2 : F
  250. If four forces act at a point ‘O’ as shown in the figure in a plane and if O is in equilibrium then the value of ‘θ’ & ‘P’ are
  251. A ship is moving due east with a velocity of 12 m/ sec, a truck is moving across on the ship with velocity 4 m/sec. A monkey is climbing the vertical pole mounted on the truck with a velocity of 3 m/sec. Find the velocity of the monkey as observed by the man on the shore
  252. A particle starts from the origin at t = 0 s with a velocity of 10 . 0 j ^ m / s and moves in the xy-plane with a constant acceleration of 8 . 0 i ^ + 2 . 0 j ^ ms – 2 . At what time is the x-coordinate of the particle 16 m?
  253. A particle is projected from the ground with velocity u making an angle θ with the horizontal. At half of its maximum height,
  254. A hose pipe lying on the ground shoots a stream of water upward at an angle 60 0 to the horizontal at a speed of 20 ms -1 . The water strikes a wall 20 m away at a height of
  255. A body is projected with a velocity 60 ms -1 at 30 0 to horizontal. Its initial velocity vector is
  256. A body is projected with a velocity 60 ms -1 at 30 0 to horizontal. Then velocity of the body after 3 sec is
  257. A body is projected with a velocity 60 ms -1 at 30 0 to horizontal. The displacement after 2 s is
  258. A body is thrown with velocity (4i + 3j ) metre per second. Its maximum height is (g = 10 ms –2 )
  259. A projectile is thrown at an angle of 30° with a velocity of 10 m/s. the change in velocity during the time interval in which it reaches the highest point is
  260. A stone is projected from the ground with a velocity of 14 ms –1 one second later it clears a wall 2 m high. The angle of projection is (g = 10 ms –2 )
  261. A body is projected at an angle 30° to the horizontal with a speed of 30 ms –1 . The angle made by the velocity vector with the horizontal after 1.5 s is (g = 10 ms –2 )
  262. Two bodies are thrown from the same point with the same velocity of 50 ms –1 . If their angles of projection are complimentary angles and the difference of maximum heights is 30 m, their maximum heights (g = 10 ms -2 )
  263. A ball is projected obliquely with a velocity 49 ms –1 strikes the ground at a distance of 245 m from the point of projection. It remained in air for
  264. A gun fires a bullet at a speed of 140 ms –1 . If the bullet is to hit a target at the same level as the gun and at 1 km distance, the angle of projection may be
  265. A particle is thrown with a velocity u at an angle θ from the horizontal. Another particle is thrown with the same velocity at an angle θ from the vertical. The ratio of times of flight of the two particles will be
  266. The equation of trajectory of a projectile is . If we assume g = 10 ms –2 the range of projectile (in meters) is
  267. Two seconds after projection, a projectile is moving at 30° above the horizontal. After one more second it is moving horizontally. If g = 10ms -2 , the velocity of projection is
  268. An object is projected with a velocity of 20 ms -1 making an angle of 45 0 with horizontal. The equation for the trajectory is h = Ax – Bx 2 where ‘h’ is height, x is horizontal distance, A and B are constants. The ratio A: B is (g = 10 ms -2 )
  269. For a projectile the ratio of maximum height reached to the square of flight time is (g = 10 ms -2 )
  270. A stone is projected from the top of a tower with velocity 20 ms –1 making an angle 30 0 with the horizontal. If the total time of flight is 5 s and g = 10 ms –2 ,
  271. The speed of a projectile at its maximum height is √3/2 times its initial speed. If the range of the projectile is p times the maximum height attained by it, then p =
  272. The velocity at the maximum height of a projectile is half of its initial velocity of projection. The angle of projection is
  273. A body is projected at angle 30 0 to horizontal on a planet with a velocity of 80 ms -1 . Its time of flight is 4 seconds then acceleration due to gravity on that planet is
  274. Two particles are projected with same velocity but at angles of projection 35 0 and 55 0 . Then their horizontal ranges are in the ratio of
  275. A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 ms –1 at an angle of 30 0 with the horizontal. How far from the throwing point will the ball be at height of 10 m from the ground?
  276. A body is projected with a certain speed at angles of projection of θ and 90 – θ. The maximum height attained in the two cases are 20 m and 10 m respectively. The maximum possible range is
  277. The coach throws a base ball to a player with an initial speed of 20 ms –1 at an angle of 45 o with the horizontal. At the moment the ball is thrown, the player is 50 m from coach. The speed and the direction that the player has to run to catch the ball at the same height at which it was released in ms –1 is
  278. The velocity of projectile at the point of projection is 2 i ^ + 3 j ^ m/s. The velocity at a point where the projectile reaches the horizontal line through the point of projection is
  279. A body is projected from height of 60 m with a velocity 10 ms -1 at angle 30 0 to horizontal. The time of flight of the body is [g =10 ms -2 ]
  280. A balll is projected with 20√2 m/s at angle 45 0 with horizontal. The angular velocity of the particle at highest point of its journey about point of projection is
  281. From a point on the ground a particle is projected with initial velocity u, such that its horizontal range is maximum. The magnitude of average velocity during its ascent is
  282. The potential energy of a projectile at its maximum height is equal to its kinetic energy there. If the velocity of projection is 20 ms -1 , its time of flight is (g = 10 ms -2 )
  283. A body is projected horizontally from a height of 78.4 m with a velocity 10 m/s. Then the angle made by its velocity vector with x-axis after 4 seconds is
  284. An aeroplane flying horizontally at an altitude of 490 m with a speed of 180 kmph drops a bomb. The horizontal distance at which it hits the ground is
  285. A stone is thrown horizontally with velocity g ms -1 from the top of a tower of height g metre. The velocity with which it hits the ground is (in ms –1 )
  286. Two cliff of heights 120 m and 100.4 m are separated by a horizontal distance of 16 m. If a car has to reach from the first cliff to the second, the horizontal velocity of the car should be
  287. A ball thrown horizontally with velocity v from the top of a tower of height h reaches the ground in t seconds. If another ball of double the mass is thrown horizontally with velocity 3v from the top of another tower of height 4h. If the first ball reaches the ground at a horizontal distance d, the second ball reaches the ground at a horizontal distance
  288. A ball is projected horizontally from the top of a building 19.6 m high. If the line joining the point of projection to the point where it hits the ground makes an angle of 45° to the horizontal, the initial velocity of the ball is
  289. A body is projected horizontally from the top of a hill with a velocity of 9.8 m/s. What time elapses before the vertical velocity is twice the horizontal velocity?
  290. A body is thrown horizontally from the top of a tower of 5 m height. It touches the ground at a distance of 10 m from the foot of the tower. Then initial velocity of the body is (g = 10 ms -2 )
  291. Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 m apart and of same height of 200m with the same velocity of 25 m/s. When and where will the two bullets collides. (g =10 m/s 2 )
  292. An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes 7 revolution in 100 s. The linear speed of the insect is
  293. What is approximately the centripetal acceleration (in units of acceleration due to gravity on earth, g = 10 ms – 2 ) of an aircraft flying at a speed of 400 ms – 1 through a circular arc of radius 0.6 km?
  294. A stone tied to the end of a string 100 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 22s, then the acceleration of the stone is
  295. A motor car is travelling at 60 m/s on a circular road of radius 1200 m. It is increasing its speed at the rate of 4 m / s 2 . The acceleration of the car is:
  296. A cyclist is riding with a speed of 27 km h – 1 . As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 ms – 1 every second. The net acceleration of the cyclist on the circular turn is
  297. A particle moves in a circle of radius 25 cm at two revolutions per sec. The acceleration of the particle in m / s 2 is:
  298. Two particles P and Q are located at distance r p and r Q respectively from the centre of rotating disc such that r p > r Q . The disc is rotating with constant angular acceleration. We can say
  299. The maximum range of a projectile is 500 m. If the particle is thrown up a plane is inclined at an angle of 30 0 with the same speed, the distance covered by it along the inclined plane will be:
  300. A motor boat travels certain distance down stream in 1 hr and up stream in 3 hrs. Now the angle normal to the flow at which the same boat must be rowed with same velocity in the river in order to cross the river along the least path is
  301. A body is projected from ground making an angle with horizontal. Then during the course of its flight
  302. Four projectiles are projected with the same speed at angles 20 o , 35 o , 60 o  ​and  75 o with the horizontal. The range will be the longest for the projectile whose angle of projection is
  303. A bomber plane moves horizontally with a speed of 500 m/s and a bomb released from it, strikes the ground in l0 s. Angle at which it strikes the ground will be (g = l0 m / s 2 )
  304. A fighter plane flying horizontally at an altitude of 1.5 km with speed 720 km h – l passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with muzzle speed 600 m s – l to hit the plane. (Take g: l0 m s – 2 )
  305. A motor cyclist is trying to jump across a path as shown by driving horizontally off a cliff A at a speed of 5 ms – l . Ignore air resistance and take g = l0 ms – 2 . Th” speed with which he rouches the peak -B is:
  306. A particle is projected from the ground with an initial speed of v at an angle θ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is:
  307. There are two values of time for which a projectile is to the same height. If time of flight is T. The sum of these two times is equal to:
  308. A projectile is fired at an angle of 45 0 with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection is
  309. A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration. vector a is correctly shown in
  310. A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the PQ circumference and returns to the centre along QO as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in kilometre and kilometer per hour) is
  311. Velocity vector and acceleration vector in a uniform circular motion are related as
  312. A body is projected such that it has maximum range ‘R’ in the absence of wind. If wind imparts a horizontal acceleration of g 4 then the new range is
  313. A body is projected up a smooth inclined plane with velocity V from the point A as shown in the figure. The angle of inclination is 45 o and the top is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of V? Length of inclined plane is 20 2 m.
  314. A ball is projected horizontally with a speed v from the top of plane inclined at an angle 45 0 with the horizontal. How far from the point of projection will the ball strike the plane?
  315. An object is projected at angle (other than 90 0 ) to the horizontal, from the ground. When it is at highest point of its path, magnitude of its position vector with respect to the point of projection is 2 times the maximum height reached by it. The angle of projection is
  316. A particle is projected at point A from an inclined plane with inclination angle θ as shown in figure. The magnitude of projection velocity is u and its direction is perpendicular to the plane. After some time it passes from point B which is in the same horizontal level of A, with velocity v . Then the angle between u and v will be
  317. A particle is projected from the bottom of an inclined plane of inclination 30 o . At what angle (from the horizontal) should the particle be projected to get maximum range on the inclined plane:
  318. A ball is thrown at angle α ( 90 o > α > θ ) on inclined plane as shown in figure. The minimum speed
  319. A particle is projected with a certain velocity at an angle α above the horizontal from the foot of an inclined plane of inclination 30 0 . If the particle strikes the plane normally then α is equal to:
  320. A particle is projected from a trolley car with a velocity v . If the trolley car moves with an acceleration a towards right, which of the following remain unchanged relative to both ground and trolley car?
  321. A helicopter is flying horizontally at 8 m/s at an altitude 180 m when a package of emergency medical supplies is ejected horizontally backward with a speed of 12 m/s relative to the helicopter. Ignoring air resistance what is horizontal distance between the package and the helicopter when the package hits the ground?
  322. An airplane moving horizontally with a speed of 180 km/hr drops a food packet while flying at a height of 500 m. The horizontal range is:
  323. A bomber moving horizontally with 500 m/s drops a bomb which strikes ground in 10 s. The angle of strike with horizontal is
  324. A projectile is projected at an angle of 45° to the horizontal. The slope of trajectory of the body varies with time t as
  325. A particle is thrown with a velocity of u m/s. It passes A and B as shown in figure at time t 1 = 1 s and t 2 = 3 s’ The value of u is
  326. A ball rolls off the top of a staircase with a horizontal velocity u m/s. If the steps are h metre high and b metre wide, the ball will hit the edge of the nth step, if:
  327. From the top of a tower 20 m high, a ball is thrown horizontally. If the line joining the point of projection to the point where it hits the ground makes an angle of 45 o with the horizontal, then the initial velocity of the ball is:
  328. Two particles are projected in air with speed u at angles θ 1 a n d θ 2 (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct?
  329. If a stone is to hit at a point which is at a distance d away and at a height h above the point from where the stone starts, then what is the value of initial speed u if the stone is launched at an angle θ ?
  330. Two balls are projected at an angle θ and ( 90 0 – θ ) to the horizontal with the same speed. The ratio of their maximum vertical heights is
  331. If R and H represent horizontal range and maximum height of the projectile, then the angle of projection with the horizontal is
  332. Two paper screens A and B are separated by 150 m. A bullet pierces A and B. The hole in B is 15 cm below the hole in A. If the bullet is travelling horizontally at the time of hitting A, then the velocity of the bullet at A is: (g: 10 ms – 2 ).
  333. A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same speed how much high above the ground can the cricketer throw the same ball?
  334. The range R of projectile is same when its maximum heights are h 1 and h 2 .What is the relation between R, h 1 and h 2 ?
  335. The trajectory of a projectile in a vertical plane is y = ax – bx 2 , where a and b are constants and x and y are respectively horizontal and vertical distances of the projectile from the point of projection. The maximum height attained by the particle and the angle of projection from the horizontal are:
  336. A person can throw a stone to a maximum height of h metre. The maximum distance to which he can throw the stone is:
  337. The range of a projectile launched at an angle of 15 o with horizontal is 1.5 km. The range of projectile when launched at an angle of 45 o to the horizontal is
  338. A particle is projected from a horizontal plane with a speed u at some angle. At highest point its velocity is found to be u/2. Then the maximum height attained by the projectile is
  339. Two particles A and B are projected simultaneously from the top of a tower horizontally. Particle A with velocity V and particle B with velocity 2V. If T 1 and T 2 are the times after which the particles strike the ground and R 1 and R 2 are their respective range on horizontal ground, then
  340. The time taken by a particle to slide down a smooth inclined plane is double the time it would take in falling down through a height equal to the vertical height of the plane. The inclination of the plane with horizontal is:
  341. A ball is thrown upwards and returns to the ground describing a parabolic path. Which of the following quantities remains constant ?
  342. A box containing food supplies is released from an aeroplane moving horizonially at a height of 490 m with a velocity of 180 km/hr. The box will rnove horizontalty while falling just before striking against the earth by:
  343. A body is dropped from a plane moving with constant horizontal velocity. The path of the body as seen by a person on the plane will be:
  344. A particle is thrown with the speed u at an angle α with the horizontal. When the particle makes an angle β with the horizontal, its speed will be:
  345. A body is projected at such angle that the horizontal range is three times the greatest height. The angle of projection is :
  346. Two projectiles of same mass and with same velocity, are thrown at an angle 60° and 30° with the horizontal, then which quantity will remain same ?
  347. A particle is projected from ground with velocity u = 40 i ^ + 30 j ^ m / s . Then range of the projectile is (Take g = 10 m/s 2 )
  348. Equation of trajectory of a projectile is given by y = 8 x − x 2 5 where x and y are in metre. If g = 10 m / s 2 , time of flight is
  349. A particle is projected from ground with a velocity of 40 m/s making an angle of 30 o with horizontal. Then
  350. A body is projected vertically upwards with a velocity of 40 m/s from a truck moving horizontally with velocity V. At the end of time of flight of the body the distance covered by the truck is 128 m. Find V
  351. A truck is moving with velocity u. An object is projected from the truck with velocity u making an angle of 60 o with horizontal as seen from the truck. What is the angle of projection as seen from ground?
  352. A body is projected from a point on ground. If just crosses a wall of height 20 m at a distance 20 m from the point of projection. If the body strikes the ground at a distance of 60 m, from the wall, the angle of projection is tan 37 o = 3 4
  353. Two particle are projected from the same point with same speed in same vertical plane but at different angles of projection such that they produce the same range. If the ratio of their times of flight is 3 : 1 , their angles of projection are
  354. A body is projected from corner A of a hall of length 16 m and height 4 m with velocity u at an angle α with horizontal such that it just touches the roof and hits the other-end B of the floor. Then ‘u’ is equal to
  355. A particle is moving in a plane in such a way that magnitude of its acceleration is constant. Then
  356. A body is projected with a velocity of 40 m/s such that its range is 4 / 3 times the maximum height attained by it. If g = 10 m/s 2 , the time of flight is
  357. A particle is projected from the origin at u = 10 i ^   m / s . It moves in the xy plane with acceleration a = 3 j ^ − 2 i ^ m / s 2 when velocity of the particle is parallel to y-axis, its speed is
  358. A body is projected from a point on ground with velocity 40 m/s. If the velocity of projection and the velocity with which it strikes the ground are mutually perpendicular, then maximum height attained by the body is
  359. A particle is projected with velocity u = 4 i ^ + 3 j ^ m / s then the radius of curvature of its trajectory at the highest position is (Take g = 10 m/s 2 )
  360. A body is projected horizontally from the top of a tower with velocity 20 m/s. Then the time after which the magntiude of its velocity becomes 40 m/s.
  361. A particle is moving along a circular path of radius r with uniform speed V. Then magnitude of average velocity of the particle during the time interval when it moves from A to B is
  362. A body is projected from a point on ground making an angle of 60 o with horizontal. If radius of curvature of its trajectory at the top most point is 10 m, then radius of curvature at the point of projection is
  363. A body is projected from ground making an angle α with horizontal. If crosses a horizontal line during its upward motion and downward motion at times t = 3 sec and t = 5 sec respectively. Then height of the line above the ground is
  364. A body is projected from ground making an angle with horizontal. Its trajectory is as shown in figure. Average velocity of the particle during its journey from A to B is V 1 , from C to D is V 2 and E to F is V 3 . Then
  365. A particle is projected from ground with velocity 20 m/s making an angle of 60 o with horizontal. Then angular velocity of the position vector of the particle just before it strikes the ground is
  366. The velocity of a particle is given by v = v 0 sin ω t v 0 is constant and ω = 2 π / T . Find the average velocity in time interval t = 0 to t = T/2.
  367. The trajectory of a projectile in a vertical plane is y = a x − b x 2 , where a and b are constants and x and y are respectively horizontal and vertical distances of the projectile from the point of projection. The maximum height attained by the particle and the angle of projection from the horizontal are :
  368. What is the average velocity of a projectile between the instants is crosses half the maximum height? It is projected with a speed u at an angle θ with the horizontal :
  369. A truck travelling due north at 20 ms -1 turns west and travels with same speed. What is the change in velocity?
  370. A ball is projected from the ground at angle θ with the horizontal. After 1s it is moving at angle 45° with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball?
  371. Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component keeping highest first.
  372. Two paper screens A and B are separated by a distance of 100 m. A bullet pierces A and then B . The hole in B is 10 cm below the hole in A . If the bullet is travelling horizontally at the time of hitting A , then the velocity of the bullet at A is
  373. The equation of trajectory of a projectile is y = 3 x – g 2 x 2 , the angle of its projection is
  374. The maximum range of a gun on horizontal terrain is 1 km. If g = 10 ms -2 , what must be the muzzle velocity of the shell?
  375. A projectile is thrown upward with a velocity v 0 at an angle α to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is
  376. Find the average velocity when a particle complete the circle of radius 1m in 10 s.
  377. Three balls of same masses are projected with equal speeds at angle 15°,45°,75°, and their ranges are respectively R 1 , R 2 andR 3 , then
  378. A body projected with velocity μ at projection angle θ has horizontal range R. For the same velocity and projection angle, its range on the moon surface will be (g moon = g earth /6)
  379. A man can throw a stone such that it acquires maximum horizontal range 80 m. The maximum height to which it will rise for the same projectile (in metre) is
  380. A projectile is thrown from a point in a horizontal plane such that the horizontal and vertical velocities are 9.8 m s – 1 and 19.6 m s – 1 . It will strike the plane after covering distance of
  381. A stone is projected in air. Its time of flight is 3 s and range is 150 m. Maximum height reached by the stone is (Take, g = 10 ms -2 )
  382. A boy throws a ball with a velocity u at an angle θ with the horizontal. At the same instant, he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of
  383. Galileo writes that for angle of projection of a projectile at angle ( 45 0 – θ ) and ( 45 0 + θ ), the horizontal ranges described by the projectile are in the ratio of (if θ ≤ 45 0 )
  384. If time of flight of a projectile is 10 s. Range is 500 m. The maximum height attained by it will be
  385. For a given velocity, a projectile has the same range R for two angles of projection. If t 1 and t 2 are the time of flight in the two cases, then t 1 t 2 is equal to
  386. The range of a projectile when launched at an angle θ is same as when launched at an angle 2 θ . What is the value of θ ?
  387. A particle is thrown with a speed u at an angle θ with the horizontal. When the particle makes an angle ϕ with the horizontal, its speed changes to ν , where
  388. An aeroplane moving horizontally with a speed of 720 kmh -1 drops a food pocket, while flying at a height of 396.9 m. The time taken by a food pocket to reach the ground and its horizontal range is (Take 9 = 9.8 ms -2 )
  389. A bullet is to be fired with a speed of 2000 ms -1 to hit a target 200 m away on a level ground. If g = 10 ms -2 , the gun should be aimed
  390. A projectile A is thrown at an angle 30° to the horizontal from point P. At the same time, another projectile B is thrown with velocity ν 2 upwards from the point Q vertically below the highest point A would reach. For B to collide with A, the ratio v 2 v 1 should be
  391. A projectile has the maximum range 500 m. If the projectile is thrown up a smooth inclined plane of 30 0 with the same (magnitude) velocity, the distance covered by it along the inclined plane till it stops will be
  392. The initial velocity of a particle of mass 2 kg is ( 4 i ^ + 4 j ^ ) ms – 1 A constant force of – 20 j ^ N is applied on the particle. Initially, the particle was at (0, 0). Find the x-coordinate of the point, where its y-coordinate is again zero.
  393. An object of mass m is projected with a momentum ρ at such an angle that its maximum height is 1/4th of its horizontal range. Its minimum kinetic energy in its path will be
  394. The equation of motion of a projectile are given by x = 36 t m and 2y = 96 t – 9.8 t 2 m. The angle of projection is
  395. Two stones are projected with same speed so as to reach the same distance from the point of projection on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the height attained by them. Then, angle of projection of the stone which attains smaller height is
  396. A ball is projected from ground with a speed of 20 m s – 1 at an angle of 45 0 with horizontal. There is a wall of 25 m height at a distance of 10m from the projection point. The ball will hit the wall at a height of
  397. A projectile can have same range from two angles of projection with same initial speed. If h 1 and h 2 be the maximum heights, then
  398. A boy can throw a stone up to a maximum height of 10m. The maximum horizontal distance that the boy can throw the same stone up to will be
  399. From the top of a tower of height 40 m, a ball is projected upwards with a speed of 20 m s – 1 at an angle of elevation of 30 0 . The ratio of the total time taken by the ball to hit the ground to the time taken to come back to the same elevation , is (Take, g = 10 m s – 2 )
  400. Two particles are simultaneously projected in opposite directions horizontally from a given point in space, where gravity g is uniform. If u 1 and u 2 and be their initial speeds, then the time t after which their velocities are mutually perpendicular is given by
  401. An object is projected with a velocity of 20 m s – 1 making an angle of 45 0 with horizontal. The equation for trajectory is h = Ax – Bx 2 , where h is height, x is horizontal distance, A and B are constants. The ratio A : B is (Take, g = 10 m s – 2 )
  402. A projectile is thrown with some initial velocity at an angle α to the horizontal. Its velocity when it is at the highest point is (2/5) 1/2 times the velocity when it is at height half of the maximum height. Find the angle of projection a with the horizontal.
  403. A body of mass 1 kg is projected with velocity 50 ms – 1 at an angle of 30 0 with the horizontal. At the highest point of its path, a force 10 N starts acting on body for 5 s vertically upward besides gravitational force. What is the horizontal range of the body? (Take, g = 10 ms – 2 )
  404. Two particles are projected from the same point with same speed u at angles of projection α and β from horizontal. The maximum heights attained by them are h 1 and h 2 respectively, R is the range for both. If t 1 and t 2 are their times of flight respectively, then which amongst the option{s) is/are incorrect?
  405. A jet aeroplane is flying at a constant height of 2 km with a speed 360 kmh – 1 above the ground towards a target and releases a bomb. After how much time, it will hit the target and what will be the horizontal distance of the aeroplane from the target, so that the bomb should hit the target? (Take, 9 = 10 ms – 1 )
  406. A particle is projected from horizontal making an angle of 53 0 with initial velocity of 100 m s – 1 . The time taken by the particle to make angle 45° from horizontal is
  407. A particle is projected from the ground at an angle θ with the horizontal with an initial speed u . Time after which velocity vector of the projectile is perpendicular to the initial velocity.
  408. For a ground-to-ground projectile, an object is at point A at t = T 3 , at point B at t = 5 T 6 and reaches the ground at t = T. The difference in heights between points A and B is
  409. A cart is moving horizontally along a straight line with a constant speed of 30 ms -1 . A projectile is to be fired from the moving cart in such a way that it will return to the cart (at the same point on cart) after the cart has moved 80 m. At what velocity (relative to the cart) must projectile be fired? (Take, g = 10 ms -2 )
  410. Two second after projection, a projectile is travelling in a direction inclined at 30 0 with the horizontal. After 1 more second, it is travelling horizontally. Then, (Take, g = 10 ms -2 )
  411. A ball rolls off top of a stair way with a horizontal velocity μ ms -1 . If the steps are h metres high and b metres wide, the ball will just hit the edge of n th step, if n equals to
  412. A hill is 500 m high. Supplies are to be sent across the hill using a canon that can hurl packets at a speed of 125 ms -1 over the hill. The canon is located at a distance of 800 m from the foot of hill and can be moved on the ground at a speed of 2 ms -1 , so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill? (Take, 9 = 10 ms -2 ) [NCERT Exemplar]
  413. Directions: These questions consists of two statements each printed as Assertion and Reason. While answering these questions you are required to choose any one of the following four responses Assertion: In case of projectile motion, the magnitude of rate of change of velocity is variable. Reason : In projectile motion, magnitude of velocity first decreases and then increases during the motion.
  414. Directions: These questions consists of two statements each printed as Assertion and Reason. While answering these questions you are required to choose any one of the following four responses Assertion: In case of projectile motion, the magnitude of rate of change of velocity is variable. Reason : In projectile motion, magnitude of velocity first decreases and then increases during the motion.
  415. Directions: These questions consists of two statements each printed as Assertion and Reason. While answering these questions you are required to choose any one of the following four responses Assertion: In case of projectile motion, the magnitude of rate of change of velocity is variable. Reason : In projectile motion, magnitude of velocity first decreases and then increases during the motion.
  416. Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 m apart and of same height of 200 m with the same velocity of 25 ms -1 . When and where will the two bullets collides? (Take, g = 10 ms -2 )
  417. Assertion The maximum height of projectile is always 25% of the maximum range. Reason For maximum range, projectile should be projected at 90°.
  418. What is the range of a projectile thrown with velocity 98 ms -1 with angle 30° from horizontal?
  419. Assertion When θ = 45° or 135°, the value of R remains the same, only the sign changes. Reason R = u 2 sin 2 θ g [AIIMS 2017]
  420. A particle is projected with an angle of projection θ to the horizontal line passing through the points (P, Q) and (Q, P) referred to horizontal and vertical axes (can be treated as X -axis and Y -axis, respectively). The angle of projection can be given by [AIIMS 2015]
  421. If the angle of projection of a projector with same initial velocity exceed or fall short of 45° by equal amount α , then the ratio of horizontal ranges is [Kerala CEE 2014]
  422. The range of a projectile is R when the angle of projection is 40°. For the same velocity of projection and range, the other possible angle of projection is
  423. A cricket ball thrown across a field is at heights h 1 and h 2 from the point of projection at times t 1 and t 2 respectively after the throw. The ball is caught by a fielder at the same height as that of projection. The time of flight of the ball in this journey is [WB JEE 2014]
  424. For an object thrown at 45° to the horizontal, the maximum height H and horizontal range R are related as
  425. A body is projected with an angle θ . The maximum height reached is h. If the time of flight is 4 s and g = 10 ms -2 , then value of h is
  426. A body is projected horizontally from the top of a tower with a velocity of 10 ms -1 . If it hits the ground at an angle of 45°, then the vertical component of velocity when it hits ground (in ms -1 ) is
  427. A particle (A) is dropped from a height and another particle (B) is thrown in horizontal direction with speed of 5 m/s from the same height. The correct statement is
  428. A ball is rolled off the edge of a horizontal table at a speed of 4 ms -1 . It hits the ground after 0.4 s. Which statement given below is true?
  429. I. In projectile motion, the angle between instantaneous velocity vector and acceleration vector can be anything between 0 to π (excluding the limiting case.) II. In projectile motion, acceleration vector is always pointing vertically downwards. (Neglect air friction). Which of the following statement{s) is/are correct?
  430. A particle is projected from ground with velocity u at angle θ from horizontal. Match the following two columns and mark the correct option from the codes given below. Column I (A) Average velocity between initial and final points (B) Change in velocity between initial final points (C) Change in velocity between initial and peak point (D) Average velocity between initial and highest points Column II (p) u sin θ (q) u cos θ (r) zero (s) None
  431. A particle is projected horizontally from a tower with velocity 10 ms -1 . Taking, g = 10 ms -2 . Match the following two columns at time t = 1 s and mark the correct option from the codes given below. Column.! (A) Horizontal component of velocity (B) Vertical component of velocity (C) Horizontal displacement (D) Vertical displacement Column.!I (p) 5 SI units (q) 10 SI unit (r) 15 SI unit (s) 20 SI unit
  432. The velocity of a projectile at the initial point A is ( 2 i ^ + 3 j ^ ) ms -1 . Its velocity (in ms -1 ) at point B is
  433. A projectile is thrown with initial velocity u 0 and angle 30° with the horizontal. If it remains in the air for 1s, what was its initial velocity?
  434. A projectile is projected at 10 ms -1 by making at an angle 60° to the horizontal. After some time, its velocity makes an angle of 30° to the horizontal. Its speed at this instant is
  435. Two particles are projected upwards with the same initial velocity v 0 in two different angles of projection such that their horizontal ranges are the same. The ratio of the heights of their highest point will be
  436. The velocity vector of the motion described by the position vector of a particle r = 2 t i ^ + t 2 j ^ is given by
  437. The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is
  438. Trajectories of two projectiles are shown in figure, let T 1 and T 2 be the periods and u 1 and u 2 are their speeds of projections, then [UP CPMT 2012]
  439. If for the same range, the two heights attained are 20 m and 80 m, then the range will be
  440. A ball thrown by one player reaches the other in 2 s. The maximum height attained by the ball above the point of projection will be (Take, g = 10 ms -2 ) [BHU 2012]
  441. A cricket fielder can throw the cricket ball with a speed ν 0 . If he throws the ball while running with speed μ at an angle θ to the horizontal, what is the effective angle to the horizontal at which the ball is projected in air as seen by a spectator?
  442. A particle is projected with a velocity of 30 ms -1 , at an angle of θ 0 = tan – 1 3 4 . After 1 s, the particle is moving at an angle θ to the horizontal, where tan θ will be equal to (Take, g = 10 ms -2 )
  443. A bomber plane moves horizontally with a speed of 500 ms -1 and a bomb released from it, strikes the ground in 10s. Angle at which it strikes the ground will be (Take, g = 10 ms -2 )
  444. Unit vector in the direction of the resultant of vectors A = – 3 i ^ – 2 j ^ – 3 k ^ and B = 2 i ^ + 4 j ^ + 6 k ^
  445. Two bodies are projected from the same point with equal speeds in such directions that they both strikes the same point on a plane whose inclination is β . If α be the angle of projection of the first body with the horizontal, the ratio of their times of flight is
  446. A particle is projected from the ground with an initial speed of v at an angle θ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is
  447. A boat is moving directly away from the gun on the shore with speed v 1 . The gun fires a shell with speed v 2 at an angle α and hits the boat. The distance of the boat from the gun at the moment it is fired is
  448. The equation of motion of projectile , projected from the top of a tower , is y = 12 x − ( 3 / 4 ) x 2 The horizontal component of velocity is 3 m/s. What is the range of projectile ? (g = 10 m / s 2 )
  449. An insect crawls a distance of 4m along north in 10 s and then a distance of 3m along East in 5s. The average velocity of the insect is:
  450. When a projectile is fired at an angle θ w.r.t. horizontal with velocity u, then its vertical component:
  451. If R is the maximum horizontal range of a particle, then the greatest height attained by it is:
  452. A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is:
  453. An artillery piece which consistently shoots its shells with the same muzzle speed has a maximum range R. To hit a target which is R 2 from the gun and on the same level, the elevation angle of the gun should be:
  454. A body has an initial velocity of 3 m/s and has an acceleration of 1 m/sec 2 normal to the direction of the initial velocity. Then, its velocity 4 seconds after the start, is:
  455. An aeroplane is flying horizontally at a height of 490 m with a velocity of 150 ms -1 . A bag containing food is to be dropped to the jawans on the ground. How far from them should the bag be dropped so that it directly reaches them?
  456. A projectile goes farthest from the earth when the angle of projection is:
  457. At what angle with the horizontal should a ball be thrown so that its range R is related to the time of flight as R = 5T 2 : (Take g = 10ms -2 )
  458. Two paper screens A and B are separated by 150 m. A bullet pierces A and then B. The hole in B is 15 cm below the hole in A. If the bullet is travelling horizontally at the time of hitting A, then the velocity of the bullet at A is: (Take g = 10 ms -2 )
  459. A projectile can have the same range R for two angles of projection. If t 1 and t 2 be the times of flight in the two cases, then what is the product of two times of flight?
  460. A projectile goes farthest from the earth when the angle an projection is:
  461. A rifle shoots a bullet with a muzzle velocity of 400 m/sec at a small target 400 metre away. The height above the target at which the bullet must be aimed to hit the target is: (Take g =10ms -2 )
  462. A projectile is fired from level ground at an angle θ above the horizontal. The elevation angle ϕ of the highest point as seen from the launch point is related to θ by the relation:
  463. A ball thrown by one player reaches the other in 2 sec. The maximum height attained by the ball above the point of projection will be about:
  464. The position of projectile launched from the origin at t = 0 is given by r = 40 i ^ + 50 j ^ m at t = 2s. If the projectile was launched at an angle θ from the horizontal, then θ is (take g = 10 m/s 2 ).
  465. The position of projectile launched from the origin at t=0 is given by r = 40   i ^ + 50 j ^ m at t = 2s. If the projectile was launched at an angle θ from the horizontal, then θ is (take g = 10 m/s 2 ).
  466. A shell is fired from a gun from the bottom of a hill along its slope. The slope of the hill is α = 30°, the angle of the barrel to the horizontal β = 60°. The initial velocity v of the shell is 21 m/s. Then, the distance of point from the gun at which shell falls is
  467. A shell is fired from a gun from the bottom of a hill along its slope. The slope of the hill is α = 30°, the angle of the barrel to the horizontal β = 60°. The initial velocity v of the shell is 21 m/s. Then, the distance of point from the gun at which shell falls is
  468. From a tower of height 19.6 m two bodies are simultaneously projected horizontally in opposite directions, with velocities of 1 m/s and 4 m/s, respectively. The horizontal distance between the two bodies when their velocity vectors are perpendicular to each other is
  469. A projectile is given an initial velocity of 5 m/s at an angle 30° below horizontal from the top of a building 25 m high. Find (a) the time after which it hits the ground; (b) the distance from the building where it strikes the ground. (g = 10 m/s 2 )
  470. Particle moves in the xy-plane with a constant acceleration g in the negative y-direction. Its equation of motion is y = ax – bx 2 , where a and b are constants. Which of the following are correct?
  471. A particle is projected with a speed v 0 at an angle θ above the horizontal surface such that the ratio of the kinetic energy at the highest point and the point of projection is 3:4. The change in velocity of the particle between these two points is
  472. Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth and one on the Moon. Which of the following three statements is/are true? I. The horizontal distance travelled by the bullet is greater for the Moon. II. The flight time is less for the bullet on the Earth. III. The velocities of the bullets at impact are the same.
  473. From a tower of height 19.6 m two bodies are simultaneously projected horizontally in opposite directions, with velocities of 1 m/s and 4 m/s, respectively. The horizontal distance between the two bodies when their velocity vectors are perpendicular to each other is
  474. A shell is fired with a horizontal velocity in the positive x-direction from the top of an 80m high cliff. The shell strikes the ground 1330 m from the base of the cliff. What is the initial speed of the shell? (Take g = 10 m/s 2 )
  475. A fighter plane flying horizontally passes over an antiaircraft gun with a uniform velocity 200 ms -1 . The gun can fire the shell with a velocity 200 2 ms − 1 . At what angle should the gun fire the shell so as to hit the plane?
  476. A particle undergoes uniform circular motion on a horizontal xy plane. At time t = 0, it moves through coordinates (3.0 m, 0) with velocity v = ( 6 .0 m / s ) j ^ . At t = 5.0 s, it moves through (11.0 m, 0) with velocity v = ( – 6 .0 m / s ) j ^ . What is its acceleration at t = 2.5 s?
  477. A particle is projected at an angle of 45° 2m from the foot of a wall, just touches the top of the wall and falls on the ground on the opposite side at a distance 4 m from it. The height of wall is :
  478. Two projectiles are thrown from the same point simultaneously with same velocity 10 ms -1 . One goes straight vertically while other at 60° with the vertical. What will be the distance of separation between the two after 1 second of their throw?
  479. Identical guns fire identical bullets horizontally at the same speed from the same height above level planes, one on the Earth and one on the Moon. Which of the following three statements is/are true? I. The horizontal distance travelled by the bullet is greater for the Moon. II. The flight time is less for the bullet on the Earth. III. The velocities of the bullets at impact are the same.
  480. A particle is projected at an angle of 45° 2m from the foot of a wall, just touches the top of the wall and falls on the ground on the opposite side at a distance 4 m from it. The height of wall is :
  481. A ball thrown by one player reaches the other in 2 sec. The maximum height attained by the ball above the point of projection will be about
  482. An aeroplane is flying horizontally at a height of 490 m with a velocity of 150 ms -1 . A bag containing food is to be dropped to the jawans on the ground. How far from them should the bag be dropped so that it directly reaches them ?
  483. A particle is thrown into air with a velocity u by making an angle θ with horizontal. Then the velocity of the projectile at the highest point is
  484. If air resistance is not considered in projectiles, the horizontal motion takes place with
  485. A ball is projected upwards from the top of a tower with a velocity of 50 ms − 1 making an angle of 30° with the horizontal. The height of the tower is 70 m. After how many seconds from the instant of throwing will the ball reach the ground ?
  486. The ceiling of a hall is 40 m high. For maximum horizontal distance, the angle at which the ball may be thrown with a speed of 56 ms -1 without hitting the ceiling of the hall is
  487. A shot is fired from a point at a distance of 200 m from the foot of a tower 100 m high so that it just passes over it. The direction of shot is
  488. A boy aims at a bird from a point at a horizontal distance of 100 m. The gun can impart a horizontal velocity of 500 m/s to the bullet. From what height above the bird, must he aim his gun in order to hit the bird? (Take g=10m / s 2 )
  489. Two projectiles of same mass and with same velocity, are thrown at an angle 60° and 30° with the horizontal, then which quantity will remain same ?
  490. A particle is projected with a velocity u making an angle θ with the horizontal. At any instant, its velocity V is at right angles to its initial velocity u ; then V is
  491. At the upper most point of a projectile, its velocity and acceleration are at an angle of
  492. A projectile has a time of flight T and range R. If the time of flight is doubled, what happens to the range ?
  493. Two particles are projected from the ground simultaneously with speeds 20 m/s and 20 / 3 m / s at an angles 30° and 60° with the horizontal in the same direction. The maximum distance between them till both of them strike the ground is approximately (g =10 m /s 2 )
  494. A body is projected at angle 30 0 to horizontal with a velocity 50 ms –1 . Its time of flight is (g=10 m/s 2 )
  495. A particle goes round a circular path with uniform velocity v. After describing half the circle, the average acceleration of the particle (if its radius is r) is
  496. A particle is projected from a horizontal plane with a velocity of 8 2 m / s at an angle. At the highest point, its velocity is found to be 8 m/s. Its range will be
  497. The range of a projectile fired at an angle of 15° is 50 m. If it is fired with the same speed at an angle of 45°,its range will be
  498. A ball is projected horizontally with a velocity of 5 m/s from the top of a building 19.6 m high. How long will the ball take to hit the ground ?
  499. A car is moving along a circular arc at a speed of 20 ms -1 . The radius of the arc is 10 m. If the speed is increased at the rate of 30 ms -2 , what is the resultant acceleration ?
  500. There are two values of time for which a projectile is at the same height. The sum of these two times is equal to
  501. A projectile is given an initial velocity of i ^ + 2 j ^ The cartesian equation of its path is : g = 10 m / s 2
  502. A ball rolls off the top of a staircase with a horizontal velocity u m/s. If the steps are h metre high and b metre wide, the ball will hit the edge of the nth step, if
  503. A ball is thrown upwards and returns to the ground describing a parabolic path. Which of the following quantities remains constant ?
  504. From the top of tower of height 20 m, two bodies are simultaneosuly projected one due north and other due west with equal speeds each of 10 m/s. Find the distance between them when they reach ground g =10 m / s 2
  505. Form the top of a tower of height 78.4 m, two stones are projected horizontally with 20 ms -1 and 30 ms -1 in opposite directions. On reaching the ground. their separation is
  506. For a projectile the ratio of maximum height reached to the square of flight time is g = 10 ms − 2 .
  507. A stone is projected with a velocity 10 2 ms − 1 at an angle of 45° to the horizontal ground. The average velocity of stone during its time of flight is
  508. The horizontal range of a projectile is 4 3 times its maximum height. Its angle of projection will be:
  509. Match the following in List – I and List – II For a projectile (R = Range, H = Maximum height, θ = angle of projection, T = time of flight) List – I List – II θ a) For height to become maximum e) 45° b) For Maximum Range f) tan -1 (4) c) For R = H g) tan -1 (2) d) For gT 2 = 4R h) 90° a b c d 1 h e f g 2 f e h g 3 h f g e 4 f h e g
  510. A ball rolls off the top of a stair case with a horizontal velocity of 4.5 ms -1 . If the steps are 0.2 metre high and 0.3 metre broad and g = 10 ms -2 , then the ball will strike the nth step where n is equal to (g=10 m/s 2 )
  511. Oblique projectile motion consists of
  512. Two thin wood screens A and B are separated by 200 m. A bullet travelling horizontally at a speed of 600 ms -1 hits the screen A, penetrates through it and finally emerges out from B making holes in A and B. If the resistance of air and wood are negligible, the difference of heights of the holes in A and B is
  513. During oblique projectile motion, the angle between velocity and acceleration
  514. The path of a oblique projectile is
  515. A stone is projected horizontally with a velocity of 40 m/s from a tower. Velocity of the body after 4 sec is (g=10 m/s 2 )
  516. Form the top of a tower of height 78.4 m, two stones are projected horizontally with 20 ms -1 and 30 ms -1 in opposite directions. On reaching the ground. their separation is
  517. A stone is projected with a velocity 10 2 ms − 1 at an angle of 45° to the horizontal ground. The average velocity of stone during its time of flight is
  518. Two bodies are thrown up, one at 45° and the other at 60°, to the horizontal. If both bodies attain the same vertical height, then the ratio of projected speed of the first projectile to that of the second projectile is
  519. Match the following in List – I and List – II For a projectile (R = Range, H = Maximum height,  = angle of projection, T = time of flight) List – I List – II θ a) For Maximum height to become maximum e) 45° b) For Maximum Range f) tan -1 (4) c) For R = H g) tan -1 (2) d) For gT 2 = 4R h) 90° a b c d 1 h e f g 2 f e h g 3 h f g e 4 f h e g
  520. Two thin wood screens A and B are separated by 200 m. A bullet travelling horizontally at a speed of 600 ms -1 hits the screen A, penetrates through it and finally emerges out from B making holes in A and B. If the resistance of air and wood are negligible, the difference of heights of the holes in A and B is
  521. A body is thrown at some angle from the ground. The magnitude of change in velocity of body in 5 s, if it is still in air, is [g = 10 m/s 2 ]
  522. An enemy plane is flying horizontally at an altitude of 2 km with a speed of 300 ms -1 . An armyman with an anti – aircraft gun on the ground sights the enemy plane when it is directly overhead and fires a shell with a muzzle speed of 600 ms -1 . At what angle with the vertical should the gun be fired so as to hit the plane ?
  523. During oblique projectile motion, the angle between velocity and acceleration
  524. A body is projected with a velocity of (3i + 4j + 5k) m/s from the ground. Taking XY-plane as ground and Z axis as vertical, its range is (g = 10 m/s 2 )
  525. The equation of trajectory of a particle is given by the equation y = ax + bx 2 where a & b are constants. Horizontal range is
  526. The path of a oblique projectile is
  527. A car travels 8 km along east, then 15 km along north and then 15 2 , km towards south-west. What will be the displacement from the starting point ?
  528. A particle is thrown with the speed u at an angle α with the horizontal. When the particle makes an angle β with the horizontal, its speed will be:
  529. A box containing food supplies is released from an aeroplane moving horizonially at a height of 490 m with a velocity of 180 km/hr. The box will rnove horizontalty while falling just before striking against the earth by:
  530. A ball is projected from the ground at angle θ with the horizontal. After 1s it is moving at angle 45° with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball?
  531. The vectors A and B are such that lA+Bl=lA-Bl then the angle between the two vectors will be

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