# Projectile Motion Worksheets

Projectile Motion:

When an object is thrown making an angle with the horizontal with some initial velocity then the object is called the projectile and it’s motion is called the projectile motion.  The study of the it’s motion is done in the study of projectiles.

Below are listed some worksheets related to  projectile motion.

You can select the best answer among the alternatives given in following MCQ or objective questions and check if you are correct or not using the answer sheet given at the bottom.

Projectile Motion Worksheets:

1. A stone is projected making acute angle with the horizontal, path of the stone is

(a) straight line

(b) circular

(c) elliptical

(d) parabolic

2. A stone is projected making an angle $90^0$ with the horizontal, the path of the stone is

(a) Straight line

(b) Circular

(c) Elliptical

(d) Parabolic

3 . A stone is released from the window of a moving train. The path of the particle as observed by a person on the ground is

(a) Straight line

(b) Circular

(c) Elliptical

(d) Parabolic

4. A stone is thrown with velocity u making an angle $\theta$ with the horizontal. The horizontal distance covered by its fall to the ground is maximum when angle$\theta$ is equal to

(a) $30^0$

(b) $90^0$

(C) $45^0$

(d) $0^0$

5. A stone is thrown with velocity u making an angle $\theta$ with the horizontal. The vertical height covered by it will be maximum when angle $\theta$ is equal to

(a) $30^0$

(b) $90^0$

(C) $45^0$

(d) $0^0$

6. An aeroplane is moving horizontally with a velocity u. It drops a packet when it is at height h. The time taken by the packet in reaching the ground will be

(a) $\sqrt{\dfrac{2h}{g}}$

(b) $\sqrt{\dfrac{2u}{g}}$

(c) $\sqrt{\dfrac{h}{2g}}$

(d) $\sqrt{\dfrac{2g}{h}}$

7. The horizontal range covered by a projectile is proportional to

(a) its velocity

(b) square of its velocity

(c) sine of angle of projection

(d) square of the sine of angle of projection.

8. The maximum height achieved by a projectile is given by (u = velocity of projection, $\theta$ = angle of projection)

(a) $\dfrac{u^2}{g}$

(b) $\dfrac{u^2 \sin 2 \theta}{g}$

(c) $\dfrac{u^2 \sin ^2 \theta}{g}$

(d) $\dfrac{u^2 \sin ^2 \theta}{2g}$

9. At the top of the trajectory of a projectile, the direction of its velocity and acceleration are

(a) parallel to each other

(b) perpendicular to each other

(c) inclined to each other at angle of $45^0$

(d) inclined to each other at angle of $60^0$

10. A ball is thrown with initial kinetic energy E at an angle $\theta$ with the horizontal. The kinetic energy of the ball at the highest point of the trajectory will be

(a) Zero

(b) $\dfrac{E}{2}$

(c) $E \cos ^2 \theta$

(d) $E \sin ^2 \theta$

11. A ball is thrown with initial kinetic energy E at an angle $60^0$ with the horizontal. The kinetic energy of the ball at the highest point of the trajectory will be

(a) Zero

(b) $\dfrac{E}{2}$

(c) $\dfrac{E}{4}$

(d) $\dfrac{3E}{4}$

12. A ball is thrown with initial kinetic energy E at an angle $60^0$ with the vertical. The kinetic energy of the ball at the highest point of the trajectory will be

(a) Zero

(b) $\dfrac{E}{2}$

(c) $\dfrac{E}{4}$

(d) $\dfrac{3E}{4}$

13. A ball is thrown with initial energy E at an angle $45^0$ with the horizontal. The kinetic energy of the ball at the highest point will be

(a) E
(b) $\dfrac{E}{2}$

(c) $\dfrac{E}{4}$

(d) $\dfrac{3E}{4}$

14. A ball is thrown with initial velocity u at an angle $\theta$ with the vertical. The velocity of the ball at the highest point will be

(a) u

(b) Zero

(c) u $\cos \theta$

(d) u $\sin \theta$

15. A point mass is projected makng an acute angle with the horizontal. If angle between velocity $\overrightarrow{v}$ and acceleration $\overrightarrow{a}$ of its path is $\theta$, then

(a) $\theta = 90^0$

(b) $\theta = 0^0$

(c) $90^0 < \theta < o^0$

(d) $0^0 < \theta < 180^0$

16. For hitting a target, one must aim the target

(a) Directly at the target

(b) Higher than target

(c) lower than target

(d) Higher or lower than target depending on velocity of projection.

17. Four balls A, B, C and D are projected with the same speed making angles $15^0 ,30^0 ,45^0$ and $60^0$ with the horizontal. Which ball will strike the ground at the farthest point?

(a) A

(b) B

(c) C

(d) D

18. In Q 17, which balls will strike the ground at the same point?

(a) A and C

(b) B and D

(c) No two balls will strike at the same point of ground

(d) All the balls strike at the same point of the ground.

19. A bullet is fired with velocity 100 m/s at an angle $30^0$ with the horizontal. The bullet will return to ground after a time interval (g= 10 m/$s^2$)

(a) 50 s

(b) 100 s

(c) 2oo s

(d) 10 s

20. In question 19, the horizontal range of bullet is

(a) 50 km

(b) 100 km

(c) 50$\sqrt{2}$ km

(d) 50$\sqrt{3}$ km

21. A body is projected with some initial velocity u at angle $\dfrac{\pi}{7}$ with the horizontal. At what another angle should the body be thrown so that the horizontal range in both cases is the same

(a) $\dfrac{\pi}{2}$

(b) $\dfrac{5 \pi }{14}$

(c) $\dfrac{4 \pi}{7}$

(d) $\dfrac{6 \pi}{7}$

22. A player kicks a ball at an angle $\theta$ with horizontal. The maximum horizontal range corresponds to an angle of

(a) $30^0$

(b) $45^0$

(c) $60^0$

(d) $75^0$

23. A cricket player hits a pitched ball at some height from ground. The angle of projection for maximum horizontal range must be

(a) $30^0$

(b) $45^0$

(c) Slightly less than $45^0$

(d) slightly more than $45^0$

24. Two balls are projected respectively from the same point in the directions inclined at $30^0$ and $60^0$ to the horizontal . If they attain the same height, the ratio of their velocities of projections is

(a) 1 : 3

(b) 3 : 1

(c) 1 : 1

(d) 1 : $\sqrt{3}$

25. Which of the following does not change when a projectile id fired at an angle with the horizontal

(a)Momentum

(b)Kinetic energy

(c)Vertical component of velocity

(d)Horizontal component of velocity

26. Two bodies are thrown with the same initial velocity at angles $\theta$ and $\left( \frac{\pi}{2} - \theta \right)$ with the horizontal, then the maximum height will be in the ratio

(a) 1 : 1

(b) $\sin ^2 \theta : \cos 2 \theta$

(c) $\sin ^2 \theta : \cos ^2 \theta$

(d) $\sin ^2 2 \theta : \cos ^2 2 \theta$

27. In question 26, the horizontal ranges will be in the ratio

(a) 1 : 1

(b) $\sin 2 \theta : \cos 2 \theta$

(c) $\sin ^2 \theta : \cos ^2 \theta$

(d) $\sin ^2 2 \theta : \cos ^2 2 \theta$

28. The range of a particle when projected at an angle $15^2$ with the horizontal is 1.5 km. What will be its range when it is projected at an angle $45^2$ to the horizontal?

(a) 1.5 km

(b) 3.0 km

(c) 4.5 km

(d) 6.0 km

29. A particle is projected with velocity 20 m/s at an angle $30^0$ with the horizontal. After how much time the angle between velocity $\overrightarrow{V}$ and acceleration $\overrightarrow{a}$ of the projectile will be be $90^0$(g= 10 m/$s^2$)

(a) 1 sec

(b) 2 sec

(c) 1.5 sec

(d) Never

30. A projectile of mass m is thrown with a velocity v making an angle $60^0$ with the horizontal. Neglecting air resistance, the change in momentum from the departure at A to its arrival at B, along vertical direction is

projectile

(a) 2 mv

(b) $\sqrt{3} mv$

(c) mv

(d) $\dfrac{mv}{\sqrt{3}}$

31. A cannon on the level plane is aimed at an angle $\theta$ above the horizontal and a shell is fired with a muzzle velocity $v_0$ towards the vertical cliff at a distance R away. The height from the bottom at which the shell strikes the side walls of the cliff is

(a) $R \tan \theta - \dfrac{g R^2}{2v_o^2 \cos ^2 \theta}$

(b) $R \tan \theta - \dfrac{1}{2} g \dfrac{g R^2}{v_0^2 }$

(c) $R \sin \theta - \dfrac{1}{2} \dfrac{g R^2}{v_0^2 \sin ^2 \theta}$

(d) $R \tan \theta + \dfrac{1}{2} \dfrac{g R^2}{v_0^2 \cos ^2 \theta}$

32. A projectile A is thrown at an angle $60^0$ to the horizontal from point P with velocity $v_1$. At the same time another projectile B is thrown with velocity $V_2$ from the point Q vertically below the highest point A would reach. For B to colide with A, the ratio $\dfrac{v_2}{v_1}$ should be

(a) 1

(b) 2

(c) $\dfrac{\sqrt{3}}{2}$

(d) 3

34. The velocity at the maximum height of a projectile is half of its initial velocity of projection u. Its range on horizontal plane is

(a) $\dfrac{3u^2}{g}$

(b) $\dfrac{3}{2} \dfrac{u^2}{g}$

(c) $\dfrac{u^2}{3g}$

(d) $\dfrac{\sqrt{3}}{2} \dfrac{u^2}{g}$

34. A stone is projected in air. Its time of flight is 3 seconds and the range is 150 m. The horizontal component of velocity of projection of stone is ($g= 10 m/s^2$

(a) $22.5 m/s^2$

(b) $15 m/s^2$

(c) $30 m/s^2$

(d) $50 m/s^2$

35. A stone is projected air. Its time of flight is 3 second and the range is 150 m. Maximum height reached by the stone is

(a) 11,25 m

(b) 37.5 m

(c) 37.5 m

(d) 90 m

36. The greatest height to which a man can throw is h. The greatest distance to which he can throw will be

(a) $\dfrac{h}{2}$

(b) h

(c) 2h

(d) 4h

37. A man can throw a stone 80 m away. The maximum height to which he can throw the stone is

(a) 10 m

(b) 20 m

(c) 40 m

(d) 80 m

38. A projectile is thrown with initial velocity. $(a \hat{i} + b \hat{j} ms^{-1}$. Its range of projection is twice the maximum height reached by it. Then

(a) $b= \dfrac{a}{2}$

(b) b= a

(c) b= 2a

(d) b= 4a

39. A car is moving horizontally with velocity v. A shell is fired upward with velocity u from the car. The horizontal range of the shell relative to ground is

(a) $\dfrac{2u^2 v}{g}$

(b) $\dfrac{2uv^2}{g}$

(c) $\dfrac{2u^2 v^2}{g}$

(d) $\dfrac{2uv}{g}$

40. A car is moving horizontally with velocity v. A shell is fired upward with velocity u inclined at angle $\theta$ with the horizontal. The horizontal range of the shell related to ground is

(a) $\dfrac{2u^2 v}{g}$

(b) $\dfrac{2uv^2}{g}$

(c) $\dfrac{2u^2 v^2}{g}$

(d) $\dfrac{2(v+u+ \cos \theta ) u \sin \theta}{g}$

41. A bullet is fired from  gun when the angle of elevation of the gun is $30^0$ and then another bullet when the angle of elevation is $60^0.$ It is then concluded that

(a) Horizontal range and maximum height attained by them in both cases will be the same

(b) Horizontal range in both cases will be same but maximum height attained in second case is thrice than in first case

(c) Horizontal range in both cases will be the same but maximum height attained in second case is thrice than in first case

(d) Maximum height in both cases in the same, but horizontal range in different

42. A projectile of mass 100 g is fired with a velocity 20 m/s making an angle $30^0$ with the horizontal. As it rises to the highest point, the momentum changes by

(a) $0.5 kg ms^{-1}$

(b) $1 kg ms^{-1}$

(c) $2 kg ms^{-1}$

(d) Zero

43. A base is thrown with an initial velocity of $100 ms^-1$ at an angle $30^0$ above the horizontal. How far from the throwing point will it attain its orginal level?

(a) 250 m

(b) 500 m

(c) 1000 m

(d) 866 m

44. The coordinates of a moving point at any time ‘t’ are given by $x=ct^2$ and $y=bt^2$. The speed of the particle is given by

(a) 2t (b+c)

(b) $2t \sqrt{c^2 - b^2}$

(c) $t \sqrt{c^2 + b^2}$

(d) $2t \sqrt{c^2 + b^2}$

45. A projectile is projected at angle $22.5^0$ to the horizontal with a soeed u. If another projectile of double the mass is projected with the same speed, at what angle with the horizontal must it be projected to have the same range

(a) $45^0$

(b) $11.25^0$

(c) $67.5^0$

(d) Unpredictable

46. The height y and the distance x along the horizontal plane of a projectile projected at a planet (with no atmosphere) are given by $x= 8t, y= 6t-10t^2$ where x and y are in metre and t is seconds. The angle of projection with horizontal at which projectile is projected is

(a) $\tan ^-1 \dfrac{3}{4}$

(b) $\tan ^-1 \dfrac{4}{3}$

(c) $\sin ^-1 \dfrac{3}{4}$

(d) $\cos ^-1 \dfrac{3}{4}$

47. In Q.46, the acceleration due to gravity at the planet is

(a) $5 m/s^2$

(b) $10 m/s^2$

(c) $20 m/s^2$

(d) $40 m/s^2$

48. In Q.46, the velocity with which the projectile is projected is

(a) 6 m/s

(b) 8 m/s

(c) 10 m/s

(d) Unpredicable

49. A body is projected horizontally from the top of a tower with a speed of 20 m/s. After 2 sec, its speed will be

(a) 20 m/s

(b) 40 m/s

(c)$20 \sqrt{2} m/s$

(d)$10 \sqrt{2} m/s$

50. In Q.49, the displacement of a body after two sec will be

(a)  60 m/s

(b) $20 \sqrt{3} m$

(c) $20 \sqrt{5} m$

(d) $40 \sqrt{2} m$

51. A large number of bullets are fired in all directions with the same speed v. The maximum area on the ground on which these bullets will spread is

(a) $\pi \dfrac{v^2}{g}$

(b) $\pi \dfrac{v^4}{g^2}$

(c) $\pi ^2 \dfrac{v^4}{g^2}$

(d) $\pi ^2 \dfrac{v^2}{g^2}$

Answers

1. (d)   2. (a)   3. (d)   4. (c)   5. (b)

6. (a)    7. (b)    8. (d)    9. (b)   10. (c)

11.  (c)  12. (d)   13. (b)   14. (d)   15. (d)

16. (b)   17. (c)   18. (b)  19. (b)   20. (d)

21. (b)  22. (b)   23. (c)   24. (a)   25. (d)

26. (c)   27. (a)   28. (b)   29. (a)   30. (b)

31. (a)  32. (c)   33. (d)  34. (d)   35. (a)

36. (c)   37. (c)   38. (c)   39. (d)   40. (d)

41. (c)   42. (b)   43. (d)   44. (d)   45. (c)

46. (a)   47. (c)   48. (c)   49. (c)   50. (c)

51. (b)

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