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CPP 8 Projectile Motion

1. The co-ordinates of a particle undergoing a 2-D motion varies with time as x = t3-2t2 and y = -2t + t2 +1 the time when it crosses x-axis b. the time when it crosses y-axis c. speed at t = 5 sec d. Average velocity and average acceleration between the times t1 and t2 if t1 and t2 are the time at which x-component of velocity is double of the y-component of the velocity. e. Average velocity in the interval when ax a.

Average speed and average velocity of the ball over its entire journey (till it reaches the ground) e. Time when its speed becomes half of its projection speed. 2. A batsman standing at A hits the ball towards the bowler (standing at B) at an angle of 60o with the horizontal with speed of 20m / s. The length of the pitch (AB) is 10 m. Find the speed with which the bowler should run so as to catch the ball just before it touches the ground.
d.

2.

3.

4.

5.

3. At the top of the projectile, the directions of its velocity and acceleration are a) parallel to each other b) Anti parallel to each other c) Inclined to each other an angle of 45o d) Perpendicular to each other 4. A stone is projected in air. Its time of flight is 3s and range is 150m. Maximum height reached by the stone is a) 37.5mb) 22.5mc) 90m d) 11.25m 5. If the time of flight of a projectile is 10 s and range is 500m, then the maximum height attained by it is a) 125m b ) 50m c) 100m d) 150m 6. The maximum height reached by the projectile is h. Time taken to reach the maximum height is T. If height of the projectile at any time t is h then H / h is a) (T / t) 2 b) T / t c) d)
( )

ms-2

Initially the particle is at (100m, -200m) and its initial ms-1 velocity is

Choose the correct statements


The particle crosses the x-axis at t = 12 sec b. The particle will never cross x-axis c. The particle will touch y-axis at t = 10 sec d. The particle will pass through origin e. The average velocity in first five seconds is
a.

7. A ball is projected with a velocity of 20 m / s at an angle to the horizontal. In order to have maximum range, its velocity at the highest point must be a) 10m / s b) 14m / s c) 16m / s d) 18m / s 8. The ceiling of a long hall is 25m high. What is the

Projectile Motion
1. A projectile is projected from ground with a velocity

40 m / s at 45o. Find


a. Velocity and displacement of particle at 2 sec. B. c.

maximum horizontal distance that a ball thrown with a speed of 40 m / s can go without hitting the ceiling of the hall? 9. A cricketer can throw a ball to a maximum horizontal distance of 100m. How much high above the ground can the cricketer throw the same ball?
10. Two bodies are thrown with the same initial velocity at angles and 90- with the horizontal. Their maximum heights are in the ratio a) 1: 1 b) sin: cos c) sin2: cos2 d) cos: sin

Direction of travel of the ball at 2 sec. Angle between the velocities at t = 2 sec and t = 6 sec.

11. If T1 and T2 are the time of flights for two projections with same initial velocity and complementary angles of projection, then the range of the projectile is given by a) R = 4gT1T2 b) R = 2gT1T2 c) R = (gT1T2) / 2 d) R = (gT1T2) / 4 12. If two projectiles have the same initial speed and range but different angles of projection and H1 and H2 are their max heights, then their range is
a)
13.

moving horizontally. What is the velocity of projection of the ball? a) m b) m c) m d) m 22. Two paper screens A and B are separated by a

distance of 100m. A bullet pierces A and then B. The hole in B is 10cm below the hole in A. If the bullet is traveling horizontally at the time of hitting A, then the velocity of the bullet at A is
a) 100 m / s b) 200 m / s c) 600 m / s d) 700 m / s 23. A projectile is thrown with a velocity and making an angle with vertical. It just crosses the top of two poles each of height h after 1s and 3s respectively. The maximum height of the projectile is a) 10m b) 20m c) 40m d) 5m 24. A package is dropped from an airplane horizontally with an initial velocity 10m / s from a height of 20m. If wind is imparting a horizontal acceleration of 0.1m / s2, then at what horizontal distance x from the point of dropping, should the pickup person stand?

b)

c)

d)

Three balls of same masses are projected with equal speeds at angles of 15o, 45o, 70o and their ranges are R1, R2 and R3 respectively. Then a) R1> R2> R3 b) R1 R1> R3 d) R2> R3> R1 14. A projectile has a range R and time of flight T. If the range is doubled (by increasing the speed of projection without changing the angle of projection), the time of flight will become a) bc) T / 2 d) 2T 15. The total speed (Vt) of the projectile at its greatest height is of its total speed when it is at half of its greatest height. What is the angle of projection? 16. A ball is projected from the ground with a speed of 20m / s at an angle of 45o with horizontal. There is a wall of 25m height at a distance of 10m from the point of projection. The ball will hit the wall at a height of a) 5m b) 7.5m c) 10m d) 12.5m 17. At time t = 0, a ball is projected from point A with a

velocity of 60m / s at 60o angle with horizontal. Determine the two times t1 and t2 when the velocity
of the ball makes an angle of 45o with the horizontal axis. 18. A ball is projected vertically upwards from the top

Multiple correct 25. Two particles are projected from ground with the same initial velocities at angles 60o and 30o (with horizontal). Let R1 and R2 be their horizontal ranges, H1 and H2 their maximum heights and T1 and T2 are their time of flights. Then a) b) c) d)
26. A particle is projected from ground with velocity 40

of a tower with a velocity of 50m / s making an angle of 30o with the horizontal. The height of the tower is 70m. After how many seconds from the instant of throwing, will the ball reach the ground?
a) 2 s b) 5 s c) 7s d) 9s 19. In the above problem, the horizontal distance

covered by the projectile before reaching the ground is


a) m b) m c) m d) m 20. A ball if thrown from the ground to clear the wall

m / s at 45o. At time 2 sec a) Displacement of the particle is 100m b) Vertical component of the velocity is 20m / sc) Velocity makes an angle of with vertical d) Particle is at a height of 60m from ground 27. At a height of 15m from the ground, velocity of a projectile is =. Here is vertically upwards and is along horizontal direction and g = 10m / s2, then a) Particle was projected at an angle of 45o with horizontal b) Time of flight of projectile is 4s c) Horizontal range of projectile is 100m d) Maximum height of projectile from ground is 20

3m high at a distance of 6m and falls 18m away from the wall. Find the angle of projection of ball. 21. A ball is projected from the ground at an angle with the horizontal. After 1 second it is moving at an angle of 45o with the horizontal and after 2 s it is