Velocity of the river with respect to ground is given by V 0 and width of the river is ‘d’. A swimmer swims (with respective to water) perpendicular to the current with acceleration a=2t (where t is time ) starting from rest from the origin ‘O’ at t=0. The equation of trajectory of the path following by the swimmer
An object is projected with a velocity of 20 m/s making an angle of 45 o with horizontal. The equation for the trajectory is h = A x − B x 2 where h is height, x is horizontal distance, A and B are constants. The ratio A : B is g = 10 ms − 2
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 path shown in the figure is appropriate for the
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
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?
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 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
Two bullets are fired horizontally with different velocities from the same height. Which will reach the ground first?
An aeroplane is flying with speed 60 m/s at angle 30 o with the horizontal. A shell is fired horizontally from the aeroplane. Find the direction and magnitude of velocity of the shell so that it falls vertically along a straight line with respect to the observer on the ground.
A particle is moving along a circular path. The angular velocity, linear velocity, angular acceleration, and centripetal acceleration of the particle at any instant, respectively, are ω , v , α , and a c . Which of the following relations is not correct?
Wind is blowing in the north direction at speed of 2 m/s which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him?
A train 1 moves from east to west and another train 2 moves from west to east on the equator with equal speeds relative to ground. The ratio of their centripetal accelerations a 1 a 2 relative to centre of earth is:
An aeroplane is to go along straight line from A to B, and back again. The relative speed with respect to wind is V. The wind blows perpendicular to line AB with speed v. The distance between A and B is l. The total time for the round trip is:
A cat runs along a straight line with constant velocity of magnitude v. A dog chases the cat such that the velocity of dog is always directed towards the cat. The speed of dog is ‘u’ and always constant. At the instant both are separated by distance x and their velocities are mutually perpendicular, the magnitude of acceleration of dog is.
Two balls are thrown from A and B simultaneously. Find the minimum distance between them during the motion.
The length of inclined plane is 15 m. A stone is projected with speed v 0 from point A to cross through point B. If minimum value of v 0 is 3x ms -1 . The value of x is .
River stream velocity grows in proportion to the distance from the bank and reaches its maximum velocity 2 ms -1 in the middle. Near the bank velocity is zero. The velocity of a swimmer in still water is 5 ms -1 and is directed perpendicular to river stream. The width of river is 100 m. The drifting in swimmer is 5n meter. The value of n is .
A stone is to be projected horizontally from top of a 1.7 m high pole. Calculate initial velocity of projection (in ms -1 ), if it strikes perpendicularly an inclined plane as shown in the figure.
Velocity versus displacement curve of a particle moving in straight line is shown in the figure. From a point P, d line is drawn perpendicular to displacement axis and line PR is drawn normal to the curve at P. Find the instantaneous acceleration of the particle at point P.
A particle starts from the origin at t = 0 with an initial velocity of 3.0 i ^ m / s and moves in the x − y plane with a constant acceleration 6.0 i ^ + 4.0 j ^ m / s 2 . The x -coordinate of the particle at the instant when its y–coordinate is 32m is meters.
Ship A is moving with velocity 30m/s due east and ship B with velocity 40m/s due north. Initial separation between the ships is 10km as shown in figure. After what time (in seconds) ships are closest to each other ?
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 y so that he can cross the road safely is
A stone projected with a velocity u angle θ with the horizontal reaches maximum height H 1 . When it is projected with velocity u at an angle π 2 − θ with the horizontal, it reaches maximum height H 2 . The relation between the horizontal range R of the projectile, H 1 and H 2 is
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, highest first
A particle is projected from point O with velocity u in a direction making an angle α with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is
Two seconds after projection a projectile is travelling in a direction inclined at 30 o to the horizontal after one more second, it is travelling horizontally, the magnitude and direction of its velocity are
Pankaj and Sudhir are playing with two different balls of masses m and 2m, respectively. If Pankaj throws his ball vertically up and Sudhir at an angle θ w i t h t h e v e r t i c l e , both of them stay in our view for the same period. The height attained by the two balls are in the ratio
A particle is projected with a velocity , so that its range on a horizontal plane is twice the greatest height attained. lf g is acceleration due to gravity, then its range is
A projectile is thrown in the upward direction making an angle of 60 o with the horizontal direction with a velocity of 150 ms -1 . Then the time after which its inclination with the horizontal is 45 o is
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
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
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
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
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 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 person walks at the rate of 3 km/hr. Rain appears to him in vertical direction at the rate of 3 3 km/hr. Find the magnitude and direction of true velocity of rain.
A swimmer crosses a flowing stream of width W to and fro in time t 1 . The time taken to cover the same distance up and down the stream is t 2 . lf t 3 is the time the swimmer would take to swim a distance 2W in still water, then
When a ceiling fan is switched off its angular velocity reduces to 50% while it makes 36 rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation)?
Position vector of a particle moving in xy plane at time t is r = a ( 1 − cos ω t ) i ^ + a sin ω t j ^ . The path of the particle is
A stone is projected from a horizontal plane. It attains maximum height ‘H’ and strikes a stationary smooth wall and falls on the ground vertically below the maximum height. Assuming the collision to be elastic the height of the point on the wall where ball will strike is
AB is an inclined plane of inclination 30 o with horizontal. Point O is 20 m above point A. A particle is projected horizontally from O leftwards, and it collides with the plane AB perpendicularly. Speed of the particle at the time of projection should be g = 10 m / s 2
A particle is projected vertically upwards from O with velocity v and a second particle is projected at the same instant from P (at a height h above O) with velocity v at an angle of projection θ . The time when the distance between them is minimum is
A particle starts from rest from origin and is moving in XY-plane, its component of acceleration in the direction of instantaneous velocity is a 0 = a ⋅ v ^ . where a is a constant vector of magnitude 2 ms -2 directed along Y-axis. Find its speed in ms -1 at y =1 m.
A cannon on a level plain is aimed at an angle α above the horizontal and a shell is fired with a muzzle velocity v o towards a vertical cliff a distance R away. Then the height from the bottom at which the shell strikes the side walls of the cliff is
A boy whirls a stone in a horizontal circle 2 m above the ground by means of a string 1.25 m long. The string breaks and the stone flies off horizontally, striking the ground 10 m away. What is the magnitude of the centripetal acceleration ( in m/s 2 ) during circular motion? Take g = 10 ms -2
A gun kept on a straight horizontal road is used to shoot at a car travelling on the same road away from the gun at a uniform speed of 10 2 m s – 1 . The car is at a distance of 150 m from the gun when it is fired at an angle of 45° to the horizontal. With what speed should the shell be projected so that it hits the car? Take g =10 ms -2 .
A swimmer can swim in still water with a speed of 5 ms -1 . While crossing a river his average speed is 3 ms -1 . If he crosses the river taking shortest possible path, what is the speed of flow of water ? (in ms -1 )
The initial velocity of a particle is u = ( 4 i ^ + 3 j ^ ) ms – 1 . It is moving with uniform acceleration a = ( 0 .4 i ^ + 0 .3 j ^ ) ms − 2 . The magnitude of its velocity after 10 s is
Which of the following is the correct relation between linear velocity v and angular velocity ω of a particle?
A girl riding a bicycle with a speed of 5 ms − 1 towards north direction, observes rain falling vertically down. If she increases her speed to 10 ms − 1 , rain appears to meet her at 45° to the vertical. What is the speed of the rain?
The motor of an engine is rotating about its axis with an angular velocity of 100 rev min -1 . It come to rest in 15s, after being switched off. Assuming constant angular deceleration. What are the number of revolutions made by it before coming to rest?
The position of a particle moving along x-axis varies with time ‘t’ given by x t = 10 + 8 t − 3 t 2 . Another particle is moving along the y-axis with its coordinate as a function of time given by y(t)= 5 − 8 t 3 . At t=1 s, the speed of the second particle as measured in the frame of the first particle is given as ν . Then ν in (m 2 /s 2 ) is
Starting from the origin at time t = 0, with initial velocity 5 j ^ m s − 1 , a particle moves in the x − y plane with a constant acceleration of 10 i ^ + 4 j ^ m s − 2 . At time t, its coordinates are 20 m , y 0 m . The value of t and y 0 are, respectively :
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 speeds when they reach the earth’s surface will be
AB is an inclined plane of inclination 30 ° with horizontal. Point O is 20m above point A. A particle is projected horizontally and it collides perpendicular to the plane AB . Speed of the particle, at ‘O’ must be g = 10 m/s 2
A projectile is fired with a speed u at an angle θ with the horizontal. Its speed when its direction of motion makes an angle ‘ α ‘ with the horizontal is
For a man moving on track ABC, rain drops appear to fall vertically for the path AB, and along the same line of its motion (i.e., as observed by a stationary observer) for path BC. The actual speed of rain drop is (in m/s)
For a given velocity, a projectile has the same range R for two angles of projection if t 1 and t 2 arc the times of flight in the two cases then
A cannon on a level plane is aimed at an angle θ above the horizontal and a shell is fired with a muzzle velocity vs 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 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 particle is projected from a point O with a velocity u in a direction making an angle α upward with the horizontal. After some time at point P, it is moving at right angle with its initial direction of projection. The time of flight from O to P is
A body is projected up a smooth inclined plane (length = 20 2 m ) with velocity u from the point M 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?
In horizontal level, ground to ground projectile if at any instant velocity becomes perpendicular to initial velocity, then what can you say about projection angle with horizontal?
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 o . If the particle strikes the plane normally, then α is equal to
A car is traveling on a highway at a speed of 25 m/s along x-axis. A passenger in a car throws a ball at an angle 37 o with horizontal in a plane perpendicular the motion of the car. The ball is projected with a speed of 10 m/s relative to car What may be the initial velocity of ball in unit vector notation
Velocity of a particle at time t = 0 is 2 m/s. A constant acceleration of 2 m/s 2 act on the particle for 2 s at an angle 60 o with the initial velocity. The magnitude of velocity of particle at the end of 2 s will be
Aman walks horizontally in rain with a velocity of 5 m/s. The raindrops strike on his back at angle of 45 0 with the horizontal. Then for the actual rain’s velocity
A particle is projected from ground at some angle with the horizontal. Let P be the point at maximum height H. At what height above the point P should the particle be aimed to have range equal to maximum height?
During a projectile motion, if the maximum height equals the horizontal range, then the angle of projection with the horizontal is
A projectile has a time of flight T and range R. If the time off light is doubled, keeping the angle of projection same, what happens to the range?
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 ship ,4 sailing due east with a velocity of 10 km/h happens to appear sailing due north with a velocity of 5 km/h , to a person, sitting in a moving ship B. Determine the velocity (absolute) of ship B.
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?
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
The range R of projectile is same when its maximum heights arc h 1 and h 2 . what is the relation between R, h 1 , and h 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 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 ball is projected from the ground at angle θ with the horizontal. After 1 s, it is moving at angle 45 o with the horizontal and after 2 s it is moving horizontally. What is the velocity of projection of the ball?
A hose lying on the ground shoots a stream of water upward at an angle of 60 o to the horizontal with the velocity of 16 m s -1 . The height at which the water strikes the wall 8 m away 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
If a stone is to hit at a point which is at a distance d away and at a height h (see figure) 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 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 o with the horizontal, then the angle of Projection of A 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
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 o . If the particle strikes the plane normally, then a is equal to
A body is projected horizontally from the top of a tower with initial velocity 18 m s -1 . It hits the ground at angle 45 o . what is the vertical component of velocity when strikes the ground?
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 2x from the foot of the tower. The horizontal velocity of the second body is
A plane flying horizontally at 100 m s -1 releases an object which reaches the ground in 10 s. At what angle with horizontal it hits the ground?
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 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:
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?
A particle is projected up with a velocity of v 0 = 10 m / s at an angle of θ 0 = 60 ∘ with horizontal onto an inclined plane. The angle of inclination of the plane is 30 o . The time of flight of the particle till it strikes the plane is (take g = 10 m / s 2 )
A bird is flying towards north with a 40 kmh − 1 and a train is moving with velocity 40 kmh − 1 towards east. What is the velocity of the bird noted by a man in the train?
A river is flowing from west to east at a speed of 5 m min -1 . Aman on the south bank of the river, capable of swimming at 10 m min -1 in still water, wants to swim across the river in the shortest time. Finally, he will move in a direction
A boat is moving with a velocity 3 i ^ + 4 j ^ with respect to ground. The water in the river is moving with a velocity – 3 i ^ – 4 j ^ with respect to ground. The relative velocity of the boat with respect to water is
A car is moving towards east with a speed of 25 kmh -1 . To the driver of the cat, a bus appears to move towards north with a speed of 25 3 kmh − 1 .What is the actual velocity of the bus?
A man who can swim at the rate of 2 km/hr (in still river) crosses a river to a point exactly opposite on the other bank by swimming in a direction of 150 o to the flow of the water in the river. The velocity of the water current in km/hr is
A man wishes to cross a river in a boat. If he crosses the river in minimum time he takes 10 minutes with a drift of 120 m. If he crosses the river taking shortest route, he takes 12.5 minutes, find velocity of the boat with respect to water.
A jet airplane travelling from east to west at a speed of 500 km h -1 ejected out gases of combustion at a speed of 1500 km h -1 with respect to the jet plane. What is the velocity of the gases with respect to an observer on the ground?
A swimmer crosses the river along the line making an angle of 45 o with the direction of flow. Velocity of the river water is 5 m/s. Swimmer takes 12 seconds to cross the river of width 60 m. The velocity of the swimmer with respect to water will be
A particle is moving along a circular path with uniform speed. Through what angle does its angular velocity change when it completes half of the circular path?
A body is moving in a circular path with a constant speed. It has
The figure shows the velocity and acceleration of a point like body at the initial moment of its motion. The acceleration vector of the body remains constant. The minimum radius of curvature of trajectory of the body is
A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from P to Q is ∠ P O Q = 40 ∘
A car is travelling with linear velocity v on a circular road of radius r. If it is increasing its speed at the rate of ‘ a’ meter/sec 2 , then the resultant acceleration will be
The angular velocity of a particle moving in a circle of radius 50 cm is increased in 5 min from 100 revolutions per minute to 400 revolutions per minute. Find the tangential acceleration of the particle.
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
A particle moves in xy plane. The position vector at any time / is r = ( 2 t ) i ^ + 2 t 2 j ^ m . The rate of change of θ at time t = 2 second (where θ is the angle which its velocity vector makes with positive x-axis) is
The diagram shows a CD rotating clockwise (as seen from above) in the CD-player. After turning it off, the CD slows down. Assuming it has not come to a stop yet, the direction of the acceleration of point P at this instance is
In uniform circular motion which of the following remains constant?
Two particles are projected from the same point with the same speed at different angles θ 1 and θ 2 to the horizontal. They have the same range. Their times of flight are t 1 and t 2 respectively.
Three stones A, B and C are simultaneously projected from same point with same speed. A is thrown upwards, B is thrown horizontally and C is thrown downwards from a building. When the distance between stone A and C becomes 10 m, then distance between A and B will be
Rain is falling with speed 12 2 , m/s at an angle of 45 o with vertical line. A man in a glider going at a speed of u at angle of 37 o with respect to ground. Find the speed of glider so that rain appears to him falling vertically. Consider motion of glider and rain drops in same vertical plane.
A stone projected at an angle of 60 o from the ground level strikes at an angle of 30 o on the roof of a building of height ‘h’ . Then the speed of projection of the stone is:
An aircraft moving with a speed of 972 km/h is at a height of 6000 m, just overhead of an anti-aircraft gun. If the muzzle velocity of the gun is 540 m/s, the firing angle θ for the bullet to hit the aircraft should be
Two guns are mounted (fixed) on two vertical cliffs that are very high from the ground as shown in figure. The muzzle velocity of the shell from G 1 is u 1 and that from G 2 is u 2 . The guns aim exactly towards each other The ratio u 1 : u 2 such that the shells collide with each other in air is (Assume that there is no resistance of air)
A particle A is projected from the ground with an initial velocity of 10 m/s at an angle of 60 o with horizontal. 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
Canon A is located on a plain a distance L from a wall of height H. On top of this wall is an identical cannon (cannon B). Ignore air resistance throughout this problem. Also ignore the size of the cannons relative to L and H. The two groups of gunners aim the cannons directly at each other. They fire at each other simultaneously, with equal muzzle speed v 0 . What is the value of v 0 for which the two cannon balls collide just as they hit the ground?
A ball is projected horizontally from an incline so as to strike a cart sliding on the incline. Neglect height of cart and point of projection of ball above incline. At the instance the ball is thrown, the speed of cart is v (in m/s). Find v so that the ball strikes the cart.
A particle is moving in XY-plane. It starts to move from origin O at an angle a with X-axis. It has a constant acceleration in negative Y-direction. After some time it passes through a point B in a direction making angle β with the X-axis. If OB makes θ = 45 ∘ angle with the X-axis, the value of tan α + tan β is .
A stone is projected from top of a vertical pole of height 3 m with initial velocity 10 ms -1 . The maximum range on the ground is 10 x m . The value of x is .
A small ball is to be thrown, so as to just pass through three equal rings of diameter 2m and placed in parallel vertical planes at distance 8 m apart with their highest points at height 32 m above the point of projection as shown in the figure. If the angle of projection with horizontal is α . The value of tan α is .
Two particles A and B are projected from point O with equal speeds. They both hit the point P of an inclined plane of inclination 15 o . Particle A is projected at an angle 30 o with inclined plane. If the ratio of time of flight of particles A and B is 1 : n . The value of n is .
A lift is going up with an acceleration 2 ms -2 . A stone is thrown upward from its floor making angle 15 o with horizontal with a speed of 4 3 ms − 1 with respect to lift. Find the horizontal range (in meter) inside the elevator.
A cat moves uniformly with speed 5 ms -1 , so that it is always headed towards a rat is moving on a straight line with constant velocity 3 ms -1 . At initial moment, their velocities are perpendicular to each other and they are separated a distance 16 m apart. Find the time (in second) after which cat catches the rat.
A stone A is thrown at an angle of 45 o to the horizontal. Another stone B is thrown with 20 ms -1 horizontally as shown in figure. They collide in mid-air. If distance BC is 4n meter, then the value of n is .
A car 2 m wide is parked along the edge of a road. At the instant, the car is started, a boy standing 6 m ahead of the car begins to cross the road with constant speed vs. If the acceleration of the car 1.5 ms -2 and if it continues to move along the edge, then the minimum value of v 0 = ( n ) 1 2 ms − 1 for which boy can avoid collide. The value of n is
A swimmer is approaching the shore with a speed of 5 3 ms − 1 . At the instant when it is at a distance of 30 3 m from the shore, he projects a ball at an elevation of 30 o for it to just reach the shore. The speed of stone relative to swimmer is 5x ms -1 . The value of x is .
A toy train moves due north at a constant speed 2 m/s along a straight track which is parallel to the wall of a room. The wall is to the east of the track at a distance 4 m. There is a toy dart gun on the train with its barrel fixed in a plane perpendicular to the motion of the train. The gun points at an angle 60 o to the horizontal. There is a vertical line drawn on the wall, stretching from floor to ceiling, and the dart gun is fired at the instant when the line is due east of the gun. If the dart leaves the gun at speed 8 m/s relative to the gun, find the distance by which the dart misses the vertical line. That is, find how far north or south of the vertical line is the point at which the dart hits the wall.
Two particles are projected simultaneously from two points O and O’ such that 10 m is the horizontal and 5 m is the vertical distance between them as shown in the figure. They are projected at the same inclination 60 o to the horizontal with the same velocity 10 ms -1 . Find the time after which their separation becomes minimum.
A body projected along an inclined plane of angle of inclination 30° stops after covering a distance x 1 . The same body projected with the same speed stops after covering a distance x 2 , if the angle of inclination of the inclined plane is increased to 60°. The ratio x 1 /x 2 is
A body, projected with a certain kinetic energy, has a horizontal range R. The kinetic energy will be minimum at a position of the projectile when its horizontal range is
A disc of radius r = 20 cm is rotating about its axis with an angular speed of 20 rads -1 . It is gently placed on a horizontal surface which is perfectly frictionless. What is the linear speed of any point on the periphery of the disc? (in m/s)
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 figure, the time taken by the projectile to reach from A to B is t. Then the distance AB is equal to
A body is projected with velocity v 1 , from the point A as shown in figure. 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
A body is moving in a circular path with a constant speed. It has
The angular velocity of a particle moving in a circle of radius 50 cm is increased in 5 min from 100 revolutions per minute to 400 revolutions per minute. Find the tangential acceleration of the particle.
Twelve persons are initially at 12 corners of a regular polygon of 12 sides of side a. Each person now moves with a uniform speed v in such a manner that 1 is always directed towards 2,2 towards 3, 3 towards 4, and so on. The time after which they meet is
Raindrops are hitting the back of a man walking at a speed of 5 kmh -1 . If he now starts running in the same direction with a constant acceleration, the magnitude of the velocity of the rain with respect to him will
A man holds an umbrella at 30° with the vertical to keep himself dry. He, then, runs at a speed of 10 ms -1 , and find the rain drops to be hitting vertically. Study the following statements and find the correct options. i. Velocity of rain w.r.t. Earth is 20 m s -1 ii. Velocity of rain w.r.t. man is 10 3 ms − 1 iii. Velocity of rain w.r.t. Earth is 30 ms − 1 iv. Velocity of rain w.r.t. man is 10 2 ms − 1
Two particles are projected simultaneously from the same point, with the same speed, in the same vertical plane, and at different angles with the horizontal in a uniform gravitational field acting vertically downwards. A frame of reference is fixed to one particle. The position vector of the other particle, as observed from this frame, is r . Which of the following statement is correct?
A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the vertical displacement-time graph is characterised by
A ball rolls off the top of a stairway horizontally with a velocity of 4.5 ms -1 . Each step is 0.2 m high and 0.3 m wide. If g is 10 ms -2 , and the ball strikes the edge of n th step, then n is equal to
The speed of a projectile at its highest point is v 1 and at the point half the maximum height is v 2 . If v 1 v 2 = 2 5 , then find the angle of projection
Figure shows that particle A is projected ,from point P with velocity u along the plane and simultaneously another particle B with velocity v at an angle α with vertical. The particles collide at point Q on the plane. Then
A particle is thrown at time t = 0 with a velocity of 10 ms -1 at an angle 60 o with the horizontal from a point on an inclined plane, making an angle of 30 o with the horizontal. The time when the velocity of the projectile becomes parallel to the incline is
Figure shows path followed by a particle and position of a particle at any instant. Four different students have represented the velocity vectors and acceleration vectors at the given instant. Which vector diagram cannot be true in any situation? (In each figure velocity is tangential to the trajectory).
The initial and final velocities of an object are as shown in figure. Which arrows shown in given options can represent average acceleration vector?
Jai is standing on the top of a building of height 25 m he wants to throw his gun to Veeru who stands on top of another building of height 20 m at distance 15 m from first building. For which horizontal speed of projection, it is possible?
A ball is projected from a point A with some velocity at an angle 30 o with the horizontal as shown in figure. Consider a target at point B. The ball will hit the target if it is thrown with a velocity v 0 equal to
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
A particle is moving along a circular path with uniform speed. Through what angle does its angular velocity change when it completes half of the circular path?
A particle is projected from a level ground making an angle θ with the horizontal (x-direction). The vertical (y) component of its velocity changes with its x coordinate according to the graph shown in figure. Calculate θ (in degree). Take g = 10 ms -2 .
A man standing at the top of a building, throws several balls at different angles to the horizontal. All balls are thrown at speed u = 10 m/s and it was found that all of them hit the ground making an angle of 45 ∘ or larger than that with the horizontal. Find the height of the building (in meter). (Take g = 10 m/s 2 )
Two towers AB and CD are situated at distance d apart as shown in figure. AB is 20 m high and CD is 30 m high from the ground. A particle is thrown from the top of AB horizontally with a velocity of 10 ms -1 towards CD. Simultaneously, another particle is thrown from the top of CD at an angle 60 o to the horizontal towards AB with the same magnitude of initial velocity as that of the first object. The two particles move in the same vertical plane, collide in mid-air, calculate the distance d (in meter) between the towers. Take g=10ms – 2
From the top of tower of height 80 m, two stones are projected horizontally with velocities 20 ms -1 and 30 ms -1 in opposite directions. Find the distance between both the stones on reaching the ground (in 10 2 m). Take g = 10 ms – 2
A body is thrown with the velocity v 0 at an angle of θ to the horizon. Determine v 0 in ms -1 if the maximum height attained by the body is 5 m and at the highest point of its trajectory the radius of curvature is r = 3 m. Neglect air resistance. [Use 80 as 9] Take g = 10 ms – 2
A particle is projected up an inclined plane of inclination β at an elevation α to the horizontal. Find the ratio between tan α and tan β , if the particle strikes the plane horizontally.
A ball is projected from the origin. The x- and y-coordinates of its displacement are given by x = 3 t and y = 4 t − 5 t 2 . Find the velocity of projection (in ms – 1 ).
In figure, find the horizontal velocity u (in ms -1 ) of a projectile so that it hits the inclined plane perpendicularly. Given H = 6.25 m. Take g = 10 ms – 2
A student throws soft balls out of the window at different angles to the horizontal. All soft balls have the same initial speed v = 10 3 ms − 1 . It turns out that all soft balls landing velocities make angles 30 o or greater with the horizontal. Find the height h (in m) of the window above the ground. Take g = 10 ms – 2
Two boats both having a mass of 150 kg including passengers in it are at rest. A sack of mass 50 kg makes 1st boat having total mass of 200 kg. It is thrown to the second boat with a velocity whose horizontal component is 2 ms − 1 , relative to water. Calculate the distance (in m) between the boat 8.5 s. after the throw if the sack spent 0.5 s in air. Neglect the resistance of air and water.
A player kicks a ball at a speed of 20 ms -1 so that its horizontal range is maximum. Another player 24 m away in the direction of kick starts running in the same direction at the same instant of hit. If he has to catch the ball just before it reaches the ground, he should run with a velocity equal to (Take g =10 ms -2 )
The equations of motion of a projectile are given by x = 36 t m and 2 y = 96 t − 9 .8 t 2 m . The angle of the projection is
A body is projected at an angle 30° with the horizontal with velocity v 1 , from the point A. 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 the trajectory of body projected from point A. For both the bodies to collide, the value of v 1 v 2 should be .
A balloon starts rising from earth surface with constant speed v 0 . Due to wind the balloon gathers a horizontal velocity component v x = ay where a is a positive constant and y is its height above earth surface. Find the horizontal drift of balloon as a function of height.
A stone of mass 1 kg tied to a light inextensible string of length L = 10/3 m is whirling in a circular path of radius L in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension is 4 and if g is taken to be 10 ms -2 , the speed of the stone at the highest point of the circle is
A body is moving in a circular path with a constant speed. It has
In figure, the angle of inclination of the inclined plane is 30°. Find the horizontal velocity V 0 so that the particle hits the inclined plane perpendicularly.
