A projectile is fired from the surface of the earth with a velocity of 5 ms -1 and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 ms -1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in ms -2 ) (given g = 9.8m/s) 2
A projectile is projected from ground with initial velocity u = u o i ^ + v 0 j ^ . If acceleration due to gravity (g)is along the negative y-direction, then find maximum displacement in x-direction
A missile is fired for maximum range with an initial velocity of 20 m/s. If g = 10m/s 2 , then range of the missile is :
A particle of mass m is projected with velocity u making an angle of 45° with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be :
A ship A is moving westwards with a speed of 10 km h -1 and a ship B 100 km south of A, is moving northwards with a speed of 10kmh -1 . The time after which the distance between them becomes shortest, is :
An aeroplane is flying horizontally with a velocity of 600 km /h at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is
Ratio of minimum kinetic energies of two projectiles of same mass is 4 : 1. The ratio of the maximum height attained by them is also 4 : 1. The ratio of their ranges would be :
A body projected at an angle reaches a maximum height, h. The total time of flight is
Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is π 3 and maximum height reached is 102m. Then the maximum height reached by the other in meter is
A body sliding on a smooth inclined plane requires 4 s to reach the bottom, starting from rest at the top. How much time does it take to cover one-fourth the distance starting from rest at the top?
Two particles are projected with same initial velocity one makes an angle θ with horizontal while other makes an angle θ with vertical. If their common range is R, then product of their time of flight is directly proportional to :
A particle of mass 1 kg is fired with velocity 50 m/s at an angle of 60° from horizontal. It is acted by viscous force of 0.2v during its journey. The horizontal distance travelled by it in first 10 seconds is :
Rain is falling vertically with a velocity of 25 ms -1 . A woman rides a bicycle with a speed of 10 ms -1 in the north to south direction. What is the direction (angle with vertical) in which she should hold her umbrella to safe herself from rain?
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 – 5t 2 . What is the velocity of projection?
A grasshopper can jump a maximum distance 1.6 m. It spends negligible time on the ground. How far can it go in 10 s?
A ball is thrown from a point with a speed v 0 at an angle of projection θ . From the same point and at the same instant, a person starts running with a constant speed v 0 /2 to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?
A body is projected at an angle of 30° with the horizontal and with a speed of 30 ms -1 . What is the angle with the horizontal after 1.5 s ? (g = 10 ms -2 )
A projectile can have same range R for two angles of projection. It t 1 and t 2 are the times of flight in the two cases, then what is the product of two times of flight?
A body is projected up along a smooth inclined plane with velocity u from the point A as shown in Fig.. The angle of inclination is 45° 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 u? The length of inclined plane is 20 2 m.
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
If a stone is to hit at a point which is at a distance d away and at a height h (Fig.) 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 ?
A car is moving horizontally along a straight line with a uniform velocity of 25 ms -1 . A projectile is to be fired from this car in such a way that it will return to it after it has moved 100 m. The speed of the projection must be
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°. If the particle strikes the plane normally, then α is equal to
The co-ordinates of a moving particle at any time f are given by x = ct 2 and y = bt 2 The speed of the particle is given by
A large number of bullets are fired in all directions with the same speed v. What is the maximum area on the ground on which these bullets will spread ?
The angle of projection, of which the horizontal range and maximum height of projectile are equal is
The height y and the distance x along the horizontal plane bf the projectile on a certain planet (with no surrounding atmosphere) are given by y = 8 t − 5 t 2 metre and x = 6 t metre where t is in second. The velocity with which the projectile is projected is
A gun fires two bullets at 60 o at 30 o with horizontal. The bullets strike at some horizontal distance. The ratio of maximum height for the two bullets is in the ratio
A shell is fired vertically upwards with a velocity v 1 from the deck of a ship travelling at a speed of v 2 . A person on the shore observes the motion of the shell as parabola whose horizontal range is given by
A man standing on a hill top projects a stone horizontally with speed v 0 as shown in fig. (2). Taking the coordinate system as shown in figure, the coordinates of the point where the stone will hit the hill surface will be
Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is π/3 and its maximum height is y 1 , then the maximum height of the other will be
Which one of the following gives the angle made by the resultant velocity after t seconds for projectile of initial velocity u, projected at an angle θ with the horizontal ?
The equation, of motion of a projectile is y = 12 x − 3 4 x 2 . The horizontal component of velocity is 3 m/s. Given g = 10 m/s 2 . What is the range of the projectile ?
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
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 )
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 ?
A boy throws a ball upwards with velocity v 0 = 20 m/s. The wind imparts a horizontal acceleration of 4 m/s 2 to the left. The angle θ with the vertical at which the ball must be thrown, so that the ball returns to the boy’s hand is : (g = 10 m/s 2 )
A projectile has a time of flight T and range R. If the time of flight is doubled keeping the angle of projection constant , what happens to the range ?
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 ?
The equation of trajectory of a projectile is given as y = 2 x − x 2 2 . The maximum height of projectile is (Symbols have usual meanings and SI unit)
The equation of the path of a projectile is given by Y = 3 x − x 2 30 3 (x and y are in meters ). The angle of,projection and the range are respectively.
The velocity of a projectile at the initial point A is 2 i ^ + 3 j ^ m / s . It’s velocity (in m/s) at point B is
Two balls are thrown from the top of a tower of unknown height with same speed 10 m/s. One is projected at an angle 45 o above the horizontal and other is projected 45 o below the horizontal. The difference between the ranges of two projectiles is
A particle of mass m is projected from the ground with an initial speed u at an angle α with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial velocity u. The angle that the composite system makes with the horizontal immediately after the collision is
A body is projected with a velocity 20 6 m / s from a point P on an inclined plane having inclination 30 0 with horizontal making an angle of 45 0 with the plane. Then the time after which the body will strike the inclined plane is
A body is projected making an angle of 60 0 with horizontal from the base of an inclined plane having an inclination of 30 0 with horizontal. When the same body is projected vertically upward with same speed, maximum height attained by it is 45 m. Then its range on the inclined plane is
A particle is projected from ground with a velocity of 20 2 m / s making an angle of 60 o with horizontal. Then the time after which its velocity vector makes an angle of 45 o with horizontal is (Take g = 10 m / s 2 ).
A small object is projected horizontally from the top of a tower. If after 1 sec, The particle is at a height of 75 m from the ground, find its time of flight.
In the arrangement shown, the wedge W is moving to the right with constant acceleration ‘a’ and the 2kg block remains stationary relative to the wedge. All surfaces are frictionless. Then the normal reaction of the wedge on the block is g = 10 m / s 2
A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed relative to water is 3 km/h. The shortest possible time to cross the river is
Two identical projectiles are fired simultaneously as shown from the ground with the same magnitude of velocity and at the same angle with respect to the horizontal. The two projectiles collide at the highest point ‘B’ and coalesce. After how much time of firing them, they reach the ground ?
In the pulley-block arrangement shown, S is a light spring balance and the system is released from rest. If the reading of S is 30 N, the ratio M/m is (Take g = 10 m / s 2 )
A particle staring from the origin (0, 0) moves in a straight line in the (x,y) plane. Its coordinates at a later time are ( 3 , 3 ). The path of the particle makes with the x-axis an angle of:
Two particles A and B are thrown simultaneously from the same point at the same angle θ of projection but with the two different initial velocities (u + v) and (v – u) respectively. Which of the following statements will be true in respect of their motions ?
An object is projected so that it just clears two walls of height 7.5 m and with separation 50 m from each other. If the time of passing between the walls is 2.5 s, the range of the projectile will be: (g = 10 m/s 2 )
A projectile is fired at an angle of 45° with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is :
A bullet is to be fired with a speed of 2000 m s -1 to hit a target 200 m away on a level ground. If g = 10 m s -1 the gun should be aimed:
Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is π 3 and the maximum height reached by it is 102 m. Then the maximum height reached by the other in meter is:
Rain is falling with speed 12 2 m/s at an angle of 45° with vertical line. A man in a glider going at a speed of u at angle of 37° with horizontal with respect to ground. Find the speed (in n/s) of glider so that rain appears to him falling vertically. Consider motion of glider and rain drops in same vertical plane.
A ball is thrown from a point with a speed v o at an angle of projection θ . From the same point and at the same instant, a person starts running with a constant speed v o 2 to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of Projection?
If string is pulled with acceleration of 2 m/s 2 then acceleration of block is :
A shell fired from the ground is just able to cross horizontally the top of a wall 90 m away and 45 m high. The direction of projection of the shell will be
A golfer standing on level ground hits a ball with a velocity of u = 52 ms -1 at an angle α above the horizontal. If tan α = 5/12, then the time for which the ball is at least 15 m above the ground will be (take g = 10 ms- 2 )
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
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, P is equal to
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 ?
A body is moving in a circle with a speed of 1 ms -1 . This speed increases at a constant rate of 2 ms -1 every second. Assume that the radius of the circle described is 25 m. The total acceleration of the body after 2 s is
A cannon on a level plane is aimed at an angle θ above the horizontal and a shell is fired with a muzzle velocity v 0 towards a vertical cliff a distance D away, Then the height from the bottom at which the shell strikes the side walls of the cliff is
A projectile is projected with kinetic energy E. If it has the maximum possible horizontal range, then its kinetic energy at the highest point will be
From a point on the ground and a distance 2 metre from the foot of a vertical wall, a ball is thrown at an angle of 45 o which just clears the top of the wall and afterward strikes the ground at a distance 4 m on the other side. The height of the wall is
If a body ‘A’ of mass M is thrown with velocity v at an angle of 30 o to the horizontal and another body ‘B’ of the same mass is thrown with the same speed at an angle of 60 o to the horizontal, the ratio of horizontal ranges of A to B will be
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
A particle is projected at an angle of elevation α and after t second it appears to have an angle of elevation β as seen from point of projection. The initial velocity will be
A smooth inclined plane is inclined at an angle q with the horizontal. A body starts from rest and slides down the inclined surface. Then the time taken by it to reach the bottom is
A particle is projected at 60 o to the horizontal with a kinetic energy K. The kinetic energy at the highest point is
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
Two balls A and B are thrown with speeds u and u/2 respectively. Both the balls cover the same horizontal distance before returning to the plane of projection. If the angle of projection of ball B is 15 o with the horizontal, then the angle of projection of A is
The angle which the velocity vector of a projectile thrown with a velocity v at an angle θ to the horizontal will make with the horizontal after time t of its being thrown up is
A projectile is fired with velocity u making angle θ with the horizontal. What is the angular momentum of the projectile at the highest point about the starting point ? Given that mass of the projectile is m
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
If a stone is to hit 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 ?
A projectile is given an initial velocity of i ^ + 2 j ^ The cartesian equation of its path is : (g = 10 m/ s 2 )
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
Time taken by the projectile to reach from A to B is t. Then the distance AB is equal to
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
A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, travelling with a velocity ν m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity ν of the bullet is
The equations of motion of a projectile are given by x = 36 t metre and 2 y = 96 t − 9 ⋅ 8 t 2 metre. The angle of projection is
A cannon ball has a range R on a horizontal plane. If h and h’ are the greatest heights in the two paths for which this is possible, then
A cricketer hits a ball with a velocity 25 m/s at 60 o above the horizontal. How far above the ground it passes over a fielder 50m from the bat (assume the ball is struck very close to the ground)
A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of 30 o with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? g = 10 m / s 2 , sin 30 ∘ = 1 2 , cos 30 ∘ = 3 2
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
A particle of mass m is projected with a velocity u making an angle of 45 o with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height h is
A player kicks a foot ball obliquely at a speed of 20 ms -1 so that its range is maximum. Another player at a distance of 24m away in the direction of kick starts running at that instant to catch the ball. Before the ball hits the ground to catch it, the speed with which the second player has to run is (g = 10 ms -2 )
A body thrown horizontally from the top of tower strikes the ground after three seconds at an angle 45° with the horizontal. The speed with which the body was projected
The maximum height reached by a projectile is 4 meters. The horizontal range is 12 meters. Velocity of projection, in ms -1 , is (g is acceleration due to gravity)
The equation of the path of a projectile is given by Y = 3 x − x 2 30 3 (x and y are in meters ). The angle of,projection and the range are respectively.
A body thrown horizontally from the top of tower strikes the ground after three seconds at an angle 45° with the horizontal. The speed with which the body was projected
A tennis ball rolls of the top of a stair case way with a horizontal velocity u m/s. If the steps are b metre wide and h metre high, the ball will hit the edge of the n th step, if
An aeroplane is flying horizontally with a velocity of 600 km /h at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is
The maximum height reached by a projectile is 4 meters. The horizontal range is 12 meters. Velocity of projection, in ms -1 , is (g is acceleration due to gravity)
A ball is projected horizontally from the top of a tower of height H with a velocity v o . It will be moving at an angle of 60° with the horizontal after time
A player kicks a foot ball obliquely at a speed of 20 ms -1 so that its range is maximum. Another player at a distance of 24m away in the direction of kick starts running at that instant to catch the ball. Before the ball hits the ground to catch it, the speed with which the second player has to run is (g = 10 ms -2 )
The position of a projectile launched from the origin at t = 0 is given by r = ( 40 i ^ + 50 j ^ ) m at t = 2 s . If the projectile was launched at an angle θ from the horizontal, then θ is (take g = 10 ms -2 )
The figure shows the position-time (x-t) graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is
Two blocks A and B of masses 2m and m, respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively
A particle has a position vector given by r = 2 i ^ + j ^ – 2 k m and velocity vector v = i ^ – j ^ + k m/s. The angular velocity (rad/s) of the particle with respect to the origin at this instant is
A projectile is fired from the surface of the earth with a velocity of 5 m s – 1 and angle θ with the horizontal. Another projectile fired from another planet with a velocity of 3 m s – 1 at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is ( m s – 2 ) is (Given g = m s – 2
A particle is projected with a velocity u. So that its horizontal range and maximum height reached are equal. The maximum height reached is
The maximum height reached by a projectile is 4 meters. The horizontal range is 12 meters. Velocity of projection , in ms – 1 , is (g is acceleration due to gravity)
A particle is projected at an angle of 45 o . After 1 sec, it breaks into two equal parts. One part stops and the other part attains the height of 20 m after the breaking of the particle. Find the velocity of projection ( g = 10 m / s 2 )
The speed of a swimmer in still water is 20 m/s . The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is, given by
A particle is projected with a velocity 40 m/s at an angle 30 o with the horizontal. Find the change in velocity when it is at a height of 15 m from the ground, (g = 10 m / s 2 )
An airplane pilot wants to fly from city A to city B which is 1000 km due north of city A. The speed of the plane in still air is 500 km/hr. The pilot neglects the effect of the wind and directs his plane due north and 2 hours later find himself 300km due north-east of city B. The wind velocity is
A rigid ball of mass m strikes a rigid wall at 60 0 and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be
Two particles A and B are placed as shown in figure. The particle A, on the top of a tower, is projected horizontally with a velocity u and the particle B is projected along the surface towards the tower, simultaneously. If both the particles meet each other. Then the speed of projection of particle B is [Ignore any friction]
A particle is projected at angle with the horizontal and it follows a trajectory given by y = 12 x − 3 4 x 2 . Find the horizontal range of the projectile.
A ball of mass 1 kg is thrown vertically upwards and returns to the ground after 3 seconds. Another ball, thrown at 60° with vertical also stays in air for the same time before it touches the ground. The ratio of the two heights are :
A small object is projected horizontally from the top of a tower of height 40 m with a velocity of 10 m/s. Simultaneously another small object is projected from the base of the tower with a velocity of 20 m/s making an angle θ with horizontal in the same plane. If the objects collide at a point at time t, find t.
A body is projected at an angle α with horizontal. It crosses a horizontal line above the point of projection during its upward journey making an angle of θ = 45 o with horizontal. If velocity of projection is 20 m/s, and α = 60 o , find the height of the line above the point of projection.
A projectile is projected at an angle of 60 0 with the horizontal with speed of 10 m/s. The minimum radius of curvature of the trajectory described by the projectile is
The ceiling of a hall is 40 m high. Then the maximum possible range of a projectile thrown at 56 m/s without hitting the ceiling of the hall is (Take g = 9 . 8 m / s 2 )
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?
Equation of trajectory of a projectile is y = x − x 2 10 , x and y are in motion. Then velocity of projection is
A body is projected from point A on an inclined plane having inclination θ with horizontal with velocity u in a direction perpendicular to the inclined plane as shown in figure. Then range of the projectile on inclined plane is
A ball is projected from a point A with some velocity at an angle 30° with the horizontal as shown in Fig. Consider a target at point B. The ball will hit the target if it is thrown with a velocity v 0 equal to
An object is suspended from a spring balance in a lift. The reading is 240 N when the lift is at rest. If the spring balance reading now changes to 220 N, then the lift is moving
A man standing on the roof of a house of height h throws one particle vertically downwards and another particle horizontally with the same velocity u . The ratio of their velocities when they reach the earth’s surface will be
A stone is projected from the ground with velocity 50 m/s at an angle of 30 0 with the horizontal. It crosses a wall after 3 sec . How far beyond the wall the stone will strike the ground. (g=10m/ s 2 )
A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of 12 km/h, he observes that the rain is falling at an angle 60 0 with the vertical. The actual velocity of rain is
A particle is projected with velocity u = 30 i ^ + 20 j ^ m/s. Then its range is (g = 10 m/s 2 )
A particle is projected from a point on ground making an angle with horizontal. Maximum height attained by it is 80 m. Find its time of flight (Take g = 10 m/s 2 )
A particle is projected with velocity u = 20 i ^ + 30 j ^ m/s from a point on ground. Then its time of flight is (Take g = 10 m/s 2 )
For ground to ground projection range of a projectile is 240 m and its angle of projection is 45 0 . Then equation of its trajectory is
A body is projected horizontally from the top of a tower of height h = 20 m with a speed u = 20 m/s . Then the angle, measured with horizontal, at which the body will strike the ground is
When a body is projected horizontally from a point on an inclined plane having inclination 30 0 with horizontal, maximum height attained by it is found to be 20 m. When the same body is projected with same speed from a point on the same inclined plane in a direction perpendicular to the plane maximum height attained by the body with respect to the inclined plane will be
A body is projected up from the top of a tower AB of height 10 m, with a speed of 10 m/s making an angle of = 30 0 with horizontal. If g = 10 m/s 2 , the time after which it will strike the ground is
A body when projected vertically upward from ground, strikes the ground after a time of 9 sec. The same body, when projected with same speed, at an angle of 60 0 with horizontal, from the base of an inclined plane having inclination of 30 0 with horizontal, it will strike the inclined plane after a time of approximately.
Rain is falling vertically with a velocity of 25 m s – 1 . A woman rides a bicycle with a speed of 10 m s – 1 in the north to south direction. What is the direction (angle with vertical) in which she should hold her umbrella to safe herself from rain?
At what angle with the horizontal should a ball be thrown so that the range R is related to the time of flight as R = 5 T 2 ? (Take g= 10 m s – 2 )
A particle is projected horizontally from the top of a tower with velocity 20 m/s. Then the time after which its speed will be 20 2 m / s . (Take g = 10 m / s 2 )
Equation of trajectory of a particle projected from a point on ground is y = x − x 2 240 where x and y are in metre. If g = 10 m / s 2 , velocity of projection is
A man moves on a straight road with a velocity of 3 km/h. Rain is falling vertically with a speed of 3 3 k m / h . At what angle with vertical should the man hold his umbrella to protect himself from rain water?
The equation of motion of a projectile is y = 12 x − 3 4 x 2 . What is the range of the projectile?
A ball is thrown at different angles with the same speed V o from the same point on ground and it has same range in both cases. If the sum of maximum heights attained by the ball is 90m and g = 10 m / s 2 , find V o
A particle starting from rest has a constant acceleration of 4 m / s 2 for 4 seconds . It then retards uniformly for next 8 seconds and comes to rest . Average acceleration during the motion of the particle is
T wo particles are projected in air with speeds u 1 and u 2 at angles θ 1 and θ 2 (both acute) respectively to the horizontal, . If the maximum height reached by the first particle is greater than that of the second, and their time of flights are T 1 and T 2 respectively then which one of the following is correct?
A projectile has
Two light strings of length 4 cm and 3 cm are tied to a bob of weight 500 gm. The free ends of the strings are tied to pegs in the same horizontal line and separated by 5 cm. The ratio of tension in the longer string to that in the shorter string is
A mass M kg is suspended by a weightless string. The horizontal force required to hold the mass at 60 o with the vertical is
The driver of a car moving towards a rocket launching with a speed of 6 ms -1 observed that the rocket is moving with speed of 10 ms -1 .The upward speed of the rocket as seen by the stationary observer is nearly
The wind is blowing from south at 10 ms –1 , but to a cyclist it appears to be blowing from the east at 10 ms –1 . The velocity of cyclist is
A particle moving with a velocity equal to 0.4 ms -1 is subjected to an acceleration of 0.15 ms -2 for 2 seconds in a direction at right angles to the direction of motion. The magnitude of the final velocity is
The velocity of water in a river is 2 kmph, while width is 400 m. A boat is rowed from a point rowing always aiming opposite point at 8 kmph of still water velocity. On reaching the opposite bank the drift obtained is
Two ships A and B are 10km apart on a line running south to north. Ship A farther north is streaming west at 20 km/h and ship B is streaming north at 20 km/h. Their distance of closest approach and how long do they take to reach it ?
At a certain height a body at rest explodes into two equal fragments with one fragment receiving a horizontal velocity of 10 ms -1 . The time interval after the explosion for which the velocity vectors of the two fragments become perpendicular to each other is (g=10ms –2 )
A force f varies with time in accordance with the following figure.The mean force for one cycle.
A gun mounted on the top of a moving truck is aimed in the backward direction at an angle of 30 0 to the vertical. If the muzzle velocity of the bullet is 4 ms -1 , the value of speed of the truck that will make the bullet come of out vertically is
A body of mass M moving with velocity V explodes into two equal parts. If one comes to rest and the other body moves with velocity v, what would be the value of v?
A) When a body slides on rough surface, its momentum is not conserved. B) When a ball falls from a height, momentum of earth ball system is conserved. C) In case of explosion of flying bomb, momentum is conserved.
A ping-pong ball of mass m is floating in air by a jet of water emerging out of a nozzle. If the water strikes the ping-pong ball with a speed v and just after collision water falls dead, the rate of mass flow of water in the nozzle is equal to:
Two particles of same mass are projected simultaneously with same speed 20 ms –1 from the top of a tower of height 20m. One is projected vertically upwards and other projected horizontally. The maximum height attained by centre of mass from the ground will be (g = 10 ms –2 )
A particle is projected from ground making an angle of tan − 1 2 with horizontal. Find the angle between its velocity vector and horizontal ground when its height above the ground will be equal to half of the maximum height attained by it.
Rain is falling vertically. A man walking horizontally holds his umbrella at an angle of 45 o with vertical. If the man doubles his velocity, at what angle with vertical should be hold his umbrella?
Two identical smooth planks A and B are kept on ground making angles 30 o and 45 o respectively with horizontal. Two smooth blocks are simultaneously released from the top of planks A and B. If t A and t B are times taken by A and B respectively, then t A : t B is
A man can row a boat in still water at a speed V. If the width of river is d and water is flowing due south at a speed V/2; then find the drift of the boat if the man rows the boat making an angle of 60 o with respect to north.
A particle of mass 2 kg is in equilibrium under the action of three forces F 1 , F 2 and F 3 . If | F 1 | = 3 N and | F 2 | = 4 N and the angle between F 1 and F 2 is 90 o . Find the acceleration of the particle after the force F 3 is removed.
A wedge Q of mass M is placed on a horizontal frictionless surface AB and a block P of mass m is released on its frictionless slope. As P slides by a length L on this slope of inclination θ , Q would slide by a distance of
If a body A of mass M is thrown with velocity u at an angle 30° to the horizontal and another body B of same mass is thrown at an angle of 60° to the horizontal, the ratio of range of A and B will be
It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation 5 π /36 radians should strike a given target. In actual practice it was found that a hill just intervened in the trajectory. At what angle of elevation should the gun be fired to hit the target ?
A ball of mass M is thrown vertically upwards. Another ball of mass2M is thrown at an angle θ to vertical. Both of them stay in air for the same period of time. The heights attained by the two are in the ratio:
The range of a proiectile, when launched at an angle of 15 0 with the horizontal is 1.5 km. What is the range of the projectile when launched at an angle of 45° to the horizontal ?
A cricket ball is hit for a six leaving the bat at an angle of 45° to the horizontal with kinetic energy K. At the top the kinetic energy of the ball is:
A bomber is flying horizontally with a constant speed of 150 m/s at a height of 78.4 m. The pilot has to drop a bomb at the enemy target. At what horizontal distance from the target should he release the bomb ?
If R is the range of a projectile on a horizontal plane and h its maximum height, the maximum horizontal range with the same velocity of Projection is:
A particle is projected upwards with a velocity of 100 m/sec at an angle of 60° with the vertical. Find the time when the particle will move perpendicular to its initial direction, taking g = 10 m/sec 2 :
A projectile is thrown in the upward direction making an angle of 60° with the horizontal direction with a velocity of 147 m s -1 . Then the time after which its inclination with the horizontal is 45°, is:
The horizontal 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 :
A ball rolls off the top of a staircase with a horizontal velocity u m s -1 . If the steps are h meter high and w meter wide the ball will hit the edge of the nth step if:
The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = (8t – 5t 2 ) meter and x = 6t meter, where r is in seconds. The velocity of projection is:
An aeroplane is flying horizontally with a velocity of 600 km/h and at a height of 1960 m. When it is vertically above a point A on the ground a bomb is released from it. The bomb strikes the ground at point B. The distance AB is:
An artillary 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:
A bullet is fired with a gun from a tower horizontally with a velocity 400 m/s. At the same time a stone is dropped from the same tower
Two particles are projected simultaneously with different speed from the same point as shown in Figure. Select incorrect statement.
Two particles ,4 and B are shot from the same height at t = 0 in opposite directions with horizontal velocities 3 m/s and 4 m/s respectively. If they are subjected to the same vertical acceleration due to gravity(g = 9.8m/s 2 )’the distance between them when their velocity vectors become mutually perpendicular, is :
Two particles are separated at a horizontal distance X as shown in Figure. They are projected at the same line as shown in figure with different initial speeds. The time after which the horizontal distance between them becomes zero :
In the arrangement shown in figure, the ends P and Q of an unstretchable string move downwards with uniform speed u. Pulleys A and B are fixed: Mass M moves upward with a speed :
In the shown arrangement, the end P of an unstretchable string move downwards with uniform speed u. Mass M moves rightward with a speed of :
A ball is thrown from the top of 36 m high tower with velocity 5 m/s at an angle 37° above the horizontal as shown. Its horizontal distance on the ground is closest to : [g = 10m/s 2 ]
As two boats approach the Mumbai, the velocity of boat I relative to boat 2 is 10 3 kmhr -1 in a direction of 60o north of east. If boat 2 has a velocity of l5 kmhr -1 due south. What is the velocity of boat 1 ?
A projectile passes two points A and B at same height after 2 s and 6 s of its projection. Horizontal separation between the points A and B is 120 m. The horizontal range is closest to:[g=10m/s 2 ]
A 2-m wide truck is moving with a uniform speed v 0 = 8 ms -1 along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is
A man swims from a point A on one bank of a river of width 100 m. When he swims perpendicular to the water current, he reaches the other bank 50 m downstream. The angle to the bank at which he should swim, to reach the directly opposite point B on the other bank is
A swimmer wishes to cross a 500-m river flowing at 5 kmh -1 . His speed with respect to water is 3 kmh -1 . The shortest possible time to cross the river is
A particle is projected with a velocity 40 m/s at an angle 30 0 with the horizontal. The magnitude of change in velocity when it is at a height of 15 m from the ground is
A particle is projected with a velocity v 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
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 horizontally. The direction of shot with horizontal is
Two bullets are fired horizontally with different velocities from the same height. Which will reach the ground first ?
The maximum height reached by projectile is 4 m. The horizontal range is 12 m. The velocity of projection in ms -1 is (g is acceleration due to gravity)
A projectile has a time of flight T and range R. If the time of flight is doubled, keeping the angle of projection same, what happens to the range?
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 about
A ball is thrown at different angles with the same speed u and from the same point and it has the same range in both the cases. If y 1 and y 2 are the heights attained in the two cases, then y 1 + y 2 is equal to
The equation of motion of a projectile is y = 12 x − 3 4 x 2 The horizontal component of velocity is 3 ms -1 . What is the range of the projectile?
At what angle with the horizontal should a ball be thrown so that the range R is related to the time of flight as R = 5 T 2 ? (Take g= 10 ms- 2 )
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 about
A ball rolls off the top of a staircase with a horizontal velocity u ms -1 . If the steps are h metre high and b metre wide, the ball will hit the edge of the nth step, if
At a height 0.4 m from the ground, the velocity of a projectile in vector form is v = ( 6 i ^ + 2 j ^ ) ms − 1 The angle of projection is
A number of bullets are fired in all possible directions with the same initial velocity u. The maximum area of ground covered by bullets is
A projectile is thrown in the upward direction making an angle of 60° with the horizontal direction with a velocity of 150 ms -1 . Then the time after which its inclination with the horizontal is 45° is
Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is π /3 and its maximum height is h 1 then the maximum height of the other will be
A body is projected horizontally from the top of a tower with initial velocity 18 ms -1 . It hits the ground at angle 45°. What is the vertical component of velocity when strikes the ground?
A ball is projected from the ground at angle θ with the horizontal. After 1 s, 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?
A plane flying horizontally at 100 ms -1 releases ah object which reaches the ground in 10 s. At what angle with horizontal it hits the ground?
A hose lying on the ground shoots a stream of water upward at an angle of 60° to the horizontal with the velocity of 16 ms -1 . The height at which the water strikes the wall 8 m away is
There are two values of time for which a projectile is at the same height. The sum of these two times is equal to (T = time of flight of the projectile)
A rifle shoots a bullet with a muzzle velocity of 400 ms -1 at a small target 400 m away. The height above the target at which the bullet must be aimed to hit the target is (g = 10 ms -2 ).
A projectile has initially the same horizontal velocity as it would acquire if it had moved from rest with uniform acceleration of 3 ms -2 for 0.5 min. If the maximum height reached by it is 80 m, then the angle of projection is (g = 10 ms -2 )
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
A projectile is given an initial velocity of i ^ + 2 j ^ The cartesian equation of its path is (g = 10 ms- 2 ).
Two balls A and B are thrown with speeds u and u/2, respectively. Both the balls cover the same horizontal distance before returning to the plane of projection. If the angle of projection of ball B is 15° with the horizontal, then the angle of projection of A is
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 2 m is projected horizontally from the top of a tower of height 2 h, it reaches the ground at a distance 2x from the foot of the tower. The horizontal velocity of the second body is
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
In Fig., the time taken by the projectile to reach from A to B is t. Then the distance AB is equal to
A ball is projected from a point A with some velocity at an angle 30° with the horizontal as shown in Fig. Consider a target at point B. The ball will hit the target if it is thrown with a velocity v0 equal to
A body is projected with velocity v 1 from the point A as shown in Fig. At the same time, another body is projected vertically upwards from B with velocity v 2 . The point B lies vertically below the highest point of first particle. For both the bodies to collide, v 2 /v 1 should be
The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = (8t – 5t 2 ) m and x = 6t m, where t is in seconds. The velocity with which the projectile is projected at t = 0 is
It is possible to project a particle with a given velocity in two possible ways so as to make it pass through a point at a distance r from the point of projection. The product of times taken to reach this point in the two possible ways is then proportional to
From the top of a tower of height 40 m a ball is projected upwards with a speed of 20 m/sec at an angle of elevation of 30 o . Then the ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (take g = 10 m/sec 2 )
The range of a particle when launched at an angle of 15 ∘ with the horizontal is 1.5 km. What is the range of the projectile when launched at an angle of 45 o to the horizontal
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 2 h, it reaches the ground at a distance 2 x from the foot of the tower. The horizontal velocity of second body is
The friction of the air causes a vertical retardation equal to 10% of the acceleration due to gravity. Take g = 10 m/s 2 . The maximum height and time to reach the maximum height will be decreased by
The ball rolls up the inclined plane, then back down. Which is the correct acceleration – time graph?
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 points will be
A ball rolls of the top of a stair way 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
A shell of mass 2 m fired with speed u at an angle θ to the horizontal explodes at the highest point of its motion into two fragments of mass m each. If one fragment, whose initial speed is zero, falls vertically, .the distance at which the other fragment falls from the gun is given by
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 a be the angle of projection of the first body with the horizontal, the ratio of their times of flight is
A ball of mass m is thrown upward with a velocity v. If air exerts an average resisting force F, the velocity with which the ball returns back to the thrower is
A ball is thrown at different angles with the same speed u and from the same points and it has same range in both the cases. If y 1 and y 2 be the heights attained in the two cases, then y 1 + y 2 =
A projectile is thrown at a angle of 15 o with the horizontal and the range is 1.5 km. What is the range when it is projected at 45 o ?
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
A particle of mass m is projected with a velocity v making an angle of 45 o with the horizontal. The magnitude of angular momentum of the projectile about an axis of projection when the particle is at maximum height h is
A projectile is projected with initial velocity ( 6 i ^ + 8 j ^ ) m / sec If g = 10ms -2 , then horizontal range is
A particle is projected with a velocity ν , 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
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
For angles of projection of a projectile at angles 45 ∘ − θ and 45 ∘ + θ , the horizontal range described by the projectile are in the ratio of
A shell is fired from a cannon with a velocity v at an angle θ with the horizontal direction At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. The speed of the other piece immediately after the explosion is
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 ?
Two tall buildings are 30 m apart. The speed with which a ball must be thrown horizonally 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
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 )
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
There are two values of time for which a projectile is at the same height. The sum of these two times is equal to
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
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
Two projectiles are projected with the same velocity. If one is projected at an angle of 30 o and the other at 60 o to the horizontal, then ratio of maximum heights reached, is
Y-component of velocity is 20 and X-component of velocity is 10. The direction of motion of the body with the horizontal at this instant is
If retardation produced by air resistance of projectile is 1/10 of acceleration due to gravity, the time to reach maximum height
A stone is thrown at an angle e to the horizontal reaches a maximum height h. Then the time of flight of stone will be
A ball is thrown from a point with a speed v 0 at an angle of projection θ. From the same point and at the same instant a person starts running with a constant speed v 0 /2 to catch the ball. Will the person be able to catch the ball ? If yes, what should be the angle of projection ?
A particle A is projected from the ground with an initial velocity of 10 m/s at an angle of 60 o with horizontal as shown in fig. (4). From what height h should an another particle B be projected horizontally with velocity 5 m/s so that both the particles collide in ground at point C if both are projected simultaneously ?(g = 10 m/s 2 )
An arrow is shot into air. Its range is 200 m and its time of flight is 5sec. If g = 10 m/s 2 , then the horizontal component of velocity of the arrow is
A projectile can have the same range R for two angles of projection. If t 1 and t 2 be the times of flights in the two cases, then the product of the two times of flight is proportional to
Two projectiles are fired at different angles with the same magnitude of velocity, such that they have the same range. At what angles they might have been projected ?
A fighter plane enters inside the enemy territory at time t = 0, with velocity v 0 = 250 m/s and moves horizontally with constant acceleration a = 20 m/s 2 as shown in fig. (3). An enemy tank at the border, spot the plane and fires shots at an angle θ = 60 o with the horizontal and with velocity u = 600 m/s. At what altitude H of the plane it can be hitted by the shot?
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:
From a point on the ground and a distance 2 metre from the foot of a vertical wall, a ball is thrown at an angle of 45 o which just clears the top of the wall and afterward strikes the ground at a distance 4 m on the other side. The height of the wall is
A large number of bullets are fired in all directions with the same speed v. What is the maximum area on the ground on which these bullets will spread ?
A ball rolls of the top of a stair way 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
The equation of motion of projectile is y = 12 x − ( 3 / 4 ) x 2 The horizontal component of velocity is 3 m/s. What is the range of projectile ? (g = 1.0 m / s 2 )
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?
A bomb is dropped from an aeroplane when it is at a height h directly above a target. If the aeroplane is moving horizontally at a speed v, the distance by which the bomb will miss the target is given by
A body projected at an angle reaches a maximum height, h. The total time of flight is
Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is π 3 and maximum height reached is 102m. Then the maximum height reached by the other in meter is
A tennis ball rolls of the top of a stair case way with a horizontal velocity u m/s. If the steps are b metre wide and h metre high, the ball will hit the edge of the n th step, if
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 m /s 2 , then value of h is
Ratio of minimum kinetic energies of two projectiles of same mass is 4 : 1. The ratio of the maximum height attained by them is also 4 : 1. The ratio of their ranges would be :
A projectile has same range R for the two angles of projection. If T 1 and T 2 are the times of flight in two cases, then:
A ball is projected horizontally from the top of a tower of height H with a velocity v o . It will be moving at an angle of 60° with the horizontal after time
A particle is projected from the ground with an initial velocity of 20 m/s at an angle of 30° with horizontal. The magnitude of change in velocity in a time interval from t = 0 to t o = 0.5 s is : (g = 10 ms -2 )
The equation of trajectory of a projectile is given as y = 2 x − x 2 2 . The maximum height of projectile is (Symbols have usual meanings and SI unit)
The position of a projectile launched from the origin at t = 0 is given by r = ( 40 i ^ + 50 j ^ ) m at t = 2 s . If the projectile was launched at an angle θ from the horizontal, then θ is (take g = 10 ms -2 )
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 ).
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 m /s 2 , then value of h is
A projectile has same range R for the two angles of projection. If T 1 and T 2 are the times of flight in two cases, then:
A particle is projected from the ground with an initial velocity of 20 m/s at an angle of 30° with horizontal. The magnitude of change in velocity in a time interval from t = 0 to t o = 0.5 s is : (g = 10 ms -2 )
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 ).
Two blocks of 2 kg and 1 kg are in contact on a frictionless table. If a force of 3 N is applied on 2 kg block, then the force of contact between the two blocks will be
Two blocks of 2 kg and 1 kg are in contact on a frictionless table. If a force of 3 N is applied on 2 kg block, then the force of contact between the two blocks will be
A jet of liquid of cross-sectional area a strikes a wall making angle θ with the wall. The water strikes with the wall with velocity v and rebounds elastically. If density of liquid be ρ , the normal force on the wall is
he figure shows the position-time (x-t) graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is
Three blocks of masses 2 kg, 3 kg and 5 kg are connected to each other with light strings and are then placed on a smooth frictionless surface. The system is pulled with a force F from the side of the lighter mass so that it moves with an acceleration of 1 ms – 2 . T 1 and T 2 denote the tensions in the other strings. The value of F is
