Projectile Motion Worksheet 1) A baseball baseball player leads leads off the game game and hits hits a long home run. run. o The ball leaves the bat at an angle of 30.0 from the horizontal with a velocity of 40.0 m/s. How far will it travel in the air? 2) A golfer is teeing teeing off on a 170.0 170.0 m long par 3 hole. The ball leaves with a velocity of 40.0 m/s at a t 50.0 o to the horizontal. Assuming that she hits the ball on a direct path to the hole, how far from the hole will the ball land (no bounces or rolls)? 3) A punter in in a football game game kicks kicks a ball from the goal goal line at 60.0 60.0o from the horizontal at 25.0 m/s. a) What is is the hang time time of the punt? b) How far down field field does does the the ball land? 4) A cannon fires fires a cannonball cannonball 500.0 500.0 m downrange downrange when when set at a o 45.0 angle. At what velocity does the cannonball leave the cannon? 5) A lovesick lovesick lad wants wants to throw a bag of candy candy and love notes notes into into the open window of his girlfriend’s bedroom 10.0 m above. Assuming it just reaches the window, he throws the love gifts at 60.0o to the ground: a) At what what velocit velocity y should should she throw throw the the bag? b) How far from from the house is is he standing standing when he throws throws the bag? bag? 6) An object object is is punted punted at 25.0 25.0 m/s m/s [40.0 [40.0o N of E] on G’s home planet. What is the range of the object on level ground? (Use g = 18.0 m/s 2) 7) An elastic elastic loaded loaded balloon launcher launcher fires fires balloons balloons at an angle of [38.0 o N of E] from the surface of the ground. If the initial velocity is 25.0 m/s, find how far away the balloons are from the launcher when they hit the level ground again. a gain. 8) A movie stunt driver on a motorcycle motorcycle speeds horizontally off a 50.0 m high cliff. How fast (in km/h) must the motorcycle leave the cliff-top if it’s to land on the level ground below at a distance of 90.0 m from the base of the cliff?
9) A football is kicked at 37.0o to the horizontal at 20.0 m/s from the player’s hand at 1.00 m from the ground. How far did the football travel before hitting the ground? 10) The same football in #15 is kicked from the ground instead. a) Find the maximum height. b) Find the time of travel. c) How far away does it hit the ground? d) Find the velocity vector at maximum height. e) Find the acceleration vector at maximum height.
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. 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 stone is
with the horizontal, the path of the
(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
with the horizontal. The
horizontal distance covered by its fall to the ground is maximum when angle equal to
is
(a) (b) (C) (d) 5. A stone is thrown with velocity u making an angle
with the horizontal. The
vertical height covered by it will be maximum when angle
is equal to
(a) (b) (C) (d) 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)
(b)
(c)
(d) 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,
= angle of projection)
(a)
(b)
(c)
(d) 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 (d) inclined to each other at angle of 10. A ball is thrown with initial kinetic energy E at an angle with the horizontal. The kinetic energy of the ball at the highest point of the trajectory will be (a) Zero
(b) (c) (d) 11. A ball is thrown with initial kinetic energy E at an angle with the horizontal. The kinetic energy of the ball at the highest point of the trajectory will be (a) Zero
(b)
(c)
(d) 12. A ball is thrown with initial kinetic energy E at an angle with the vertical. The kinetic energy of the ball at the highest point of the trajectory will be (a) Zero
(b)
(c)
(d) 13. A ball is thrown with initial energy E at an angle kinetic energy of the ball at the highest point will be
with the horizontal. The
(a) E
(b)
(c)
(d) 14. A ball is thrown with initial velocity u at an angle of the ball at the highest point will be
with the vertical. The velocity
(a) u (b) Zero (c) u (d) u 15. A point mass is projected makng an acute angle with the horizontal. If angle between velocity
and acceleration
of its path is
(a) (b) (c) (d) 16. For hitting a target, one must aim the target (a) Directly at the target
, then
(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 at the farthest point?
and
with the horizontal. Which ball will strike the ground
(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 bullet will return to ground after a time interval (g= 10 m/ (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
with the horizontal. The )
(c) 50
km
(d) 50
km
21. A body is projected with some initial velocity u at angle with the horizontal. At what another angle should the body be thrown so that the horizontal range in both cases is the same
(a)
(b)
(c)
(d) 22. A player kicks a ball at an angle range corresponds to an angle of
with horizontal. The maximum horizontal
(a) (b) (c) (d) 23. A cricket player hits a pitched ball at some height from ground. The angle of projection for maximum horizontal range must be (a) (b) (c) Slightly less than
(d) slightly more than 24. Two balls are projected respectively from the same point in the directions inclined at and 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 : 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 with the horizontal, then the maximum height will be in the ratio (a) 1 : 1 (b) (c) (d) 27. In question 26, the horizontal ranges will be in the ratio (a) 1 : 1 (b) (c)
and
(d) 28. The range of a particle when projected at an angle km. What will be its range when it is projected at an angle
with the horizontal is 1.5 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 After how much time the angle between velocity projectile will be be
(g= 10 m/
with the horizontal.
and acceleration
of the
)
(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 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)
(c) mv
(d) 31. A cannon on the level plane is aimed at an angle above the horizontal and a shell is fired with a muzzle velocity 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)
(b)
(c)
(d) 32. A projectile A is thrown at an angle
to the horizontal from point P with
velocity . At the same time another projectile B is thrown with velocity from the point Q vertically below the highest point A would reach. For B to colide with A,
the ratio
(a) 1 (b) 2
should be
(c) (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)
(b)
(c)
(d) 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 (
(a)
(b)
(c)
(d) 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) (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. projection is twice the maximum height reached by it. Then
. Its range of
(a) (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)
(b)
(c)
(d) 40. A car is moving horizontally with velocity v. A shell is fired upward with velocity u inclined at angle ground is
with the horizontal. The horizontal range of the shell related to
(a)
(b)
(c)
(d) 41. A bullet is fired from gun when the angle of elevation of the gun is then another bullet when the angle of elevation is
and
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 with the horizontal. As it rises to the highest point, the momentum changes by
(a) (b)
(c) (d) Zero 43. A base is thrown with an initial velocity of at an angle 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 and (a) 2t (b+c) (b) (c) (d)
. The speed of the particle is given by
45. A projectile is projected at angle 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) (b) (c) (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 where x and y are in metre and t is seconds. The angle of projection with horizontal at which projectile is projected is
(a)
(b)
(c)
(d) 47. In Q.46, the acceleration due to gravity at the planet is
(a)
(b)
(c)
(d)
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)
(d) 50. In Q.49, the displacement of a body after two sec will be (a) 60 m/s (b) (c) (d) 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)
(b)
(c)
(d)
