PHYSICS-I PROJECTILE MOTION ENTRY -TEST 2023

1. The kinetic energy of projectile at 7. The relative acceleration of a

the highest point of a trajectory is projectile to another projectile is
(A) Cosθ times of its initial K.E (A) -g (B) -2g
(B) Cosθ2 times of its initial K.E (C) 2g (D) 0
(C) Sinθ2 times of its initial K.E
(D) Sinθ times of its initial K.E 8. In the motion of a projectile freely
under gravity, its
2. If 5% range of projectile is (a) Total energy is conserved
decreases by decreasing its speed of (b) Momentum is conserved
projection, at same angle of (c) Energy and momentum both are
projection. The (%) decrease in the conserved
maximum height will be (d) None is conserved
(A) 20% (B) 15% 9. The range of a projectile for a given
(C) 10% (D) 5% initial velocity is maximum when
3. If a rocket is projected with a the angle of projection is 45 o . The
velocity of 20 m/s at an angle of 60° range will be minimum, if the angle
to the vertical axis, then the of projection is
maximum height of rocket is: (a) 90O (b) 180O
(A) 20 m (B) 10m (c) 60O (d) 75O
(C) 5m (D) 15m 10. The angle of projection at which the
4. The horizontal range of a projectile horizontal range and maximum
is 𝟐 times of its maximum height. height of projectile are equal is
The angle of projection will be: (a) 45O (b)  = tan −1 (0.25)
1 1
(A) Tan−1 ( ) (B) Tan−1 ( ) (c)  = tan −1 4 (d) 60O
4 2
−1 (4) −1 (2) 11. A ball is thrown upwards and it
(C) Tan (D) Ta n
returns to ground describing a
parabolic path. Which of the
5. Which of the following relation of
following remains constant
components of velocities correct if
(a) Kinetic energy of the ball
the horizontal range of a projectile
(b) Speed of the ball
is equal of its maximum height;
(c) Horizontal component of velocity
(A) 𝑉𝑦 = 2𝑉𝑥 (B) 𝑉𝑦 = 4𝑉𝑥
(d) Vertical component of velocity
(C) 𝑉𝑦 = 𝑉𝑥/4 (D) 𝑉𝑦 = 𝑉𝑥
12. At the top of the trajectory of a
projectile, the directions of its
6. If the initial velocity of a projectile
velocity and acceleration are
be doubled, keeping the angle of
(a) Perpendicular to each other
projection same, the maximum
(b) Parallel to each other
height reached by it will
(c) Inclined to each other at an angle
(a) Remain the same
of 45O
(b) Be doubled
(d) Antiparallel to each other
(c) Be quadrupled
(d) Be halved
PHYSICS-I PROJECTILE MOTION ENTRY -TEST 2023

13. An object is thrown along a (a) h (b) h

direction inclined at an angle of 45 o 2
with the horizontal direction. The (c) 2h (d) 3h
horizontal range of the particle is 19. The horizontal range is four times
equal to the maximum height attained by a
(a) Vertical height projectile. The angle of projection is
(b) Twice the vertical height (a) 90O (b) 60O
(c) Thrice the vertical height (c) 45O (d) 30O
(d) Four times the vertical height 20. A ball is projected with kinetic
14. The range of a particle when energy E at an angle of 45 o to the
launched at an angle of 15 o with the horizontal. At the highest point
horizontal is 1.5 km. What is the during its flight, its kinetic energy
range of the projectile when will be
launched at an angle of 45 o to the (a) Zero (b) E
horizontal 2
(a) 1.5 km (b) 3.0 km (c) E (d) E
2
(c) 6.0 km (d) 0.75 km
15. A stone is projected from the 21. A particle of mass m is projected
ground with velocity 25 m / s. Two with velocity v making an angle of
45 o with the horizontal. The
seconds later, it just clears a wall 5
m high. The angle of projection of magnitude of the angular
the stone is ( g = 10m / sec2 ) momentum of the particle about the
point of projection when the
(a) 30O (b) 45O
particle is at its maximum height is
(c) 50.2O (d) 60O
(where g = acceleration due to
16. Angles of projection of a projectile
gravity)
at angles (45 +  ) and (45 −  ) , the
(a) Zero (b) mv3 / (4 2 g )
horizontal ranges described by the
projectile are in the ratio of (if   45 ) (c) mv3 / ( 2 g ) (d) mv 2 / 2 g
(a) 2 : 1 (b) 1 : 2 22. A particle reaches its highest point
(c) 1 : 1 (d) 2 : 3 when it has covered exactly one half
of its horizontal range. The
17. A projectile thrown with a speed v corresponding point on the
at an angle  has a range R on the displacement time graph is
surface of earth. For same v and  , characterised by
its range on the surface of moon (a) Negative slope and zero curvature
will be (b) Zero slope and negative curvature
(a) R / 6 (b) 6 R (c) Zero slope and positive curvature
(c) R / 36 (d) 36 R (d) Positive slope and zero curvature
18. The greatest height to which a man 23. At the top of the trajectory of a
can throw a stone is h . The greatest projectile, the acceleration is
distance to which he can throw it, (a) Maximum (b) Minimum
will be (c) Zero (d) g
PHYSICS-I PROJECTILE MOTION ENTRY -TEST 2023

24. When a body is thrown with a ratio of the maximum heights

velocity u making an angle  with reached is
the horizontal plane, the maximum (a) 3 : 1 (b) 1 : 3
distance covered by it in horizontal (c) 1 : 2 (d) 2 : 1
direction is 30. If the range of a gun which fires a
u sin 
2
u sin 2
2
shell with muzzle speed V is R , then
(a) (b) the angle of elevation of the gun is
g 2g
u sin 2
2
u cos 2
2 V2  gR 
(c) (d)
−1
(a) cos   (b) cos −1  2 
g g  Rg  V 
25. A football player throws a ball with 1V2  1 −1  gR 
(c)   (d) sin  2 
a velocity of 50 metre/sec at an angle 2  Rg  2 V 
30 degrees from the horizontal. The 31. If time of flight of a projectile is 10
ball remains in the air for (g = 10 m / s 2 ) seconds. Range is 500 meters. The
(a) 2.5 sec (b) 1.25 sec maximum height attained by it will
(c) 5 sec (d) 0.625 sec be
26. A body of mass 0.5 kg is projected (a) 125 m (b) 50 m
under gravity with a speed of 98 m/s (c) 100 m (d) 150 m
at an angle of 30 o with the 32. If a body A of mass M is thrown with
horizontal. The change in velocity V at an angle of 30 o to the
momentum (in magnitude) of the horizontal and another body B of the
body is same mass is thrown with the same
(a) 24.5 N − s (b) 49.0 N − s speed at an angle of 60 o to the
(c) 98.0 N − s (d) 50.0 N − s horizontal. The ratio of horizontal
27. A body is projected at such an angle range of A to B will be
that the horizontal range is three (a) 1 : 3 (b) 1 : 1
times the greatest height. The angle (c) 1: 3 (d) 3 :1
of projection is 33. A bullet is fired from a cannon with
(a) 25o8 (b) 33o 7 velocity 500 m/s. If the angle of
(c) 42o8 (d) 53o8 projection is 15 o and g = 10 m / s 2 . Then
28. A gun is aimed at a target in a line of the range is
its barrel. The target is released and (a) 25 103 m (b) 12.5 103 m
allowed to fall under gravity at the (c) 50 102 m (d) 25 102 m
same instant the gun is fired. The 34. A ball thrown by a boy is caught by
bullet will another after 2 sec. some distance
(a) Pass above the target away in the same level. If the angle of
(b) Pass below the target projection is 30o, the velocity of
(c) Hit the target projection is
(d) Certainly miss the target (a) 19.6 m/s (b) 9.8 m/s
29. Two bodies are projected with the (c) 14.7 m/s (d) None of these
same velocity. If one is projected at 35. A particle covers 50 m distance
an angle of 30 o and the other at an when projected with an initial
angle of 60 o to the horizontal, the
PHYSICS-I PROJECTILE MOTION ENTRY -TEST 2023

speed. On the same surface it will height attained by the ball above
cover a distance, when projected the point of projection will be about
with double the initial speed (a) 10 m (b) 7.5 m
(a) 100 m (b) 150 m (c) 5 m (d) 2.5 m
(c) 200 m (d) 250 m 41. In a projectile motion, velocity at
36. A ball is thrown upwards at an maximum height is
angle of 60o to the horizontal. It (a) u cos  (b) u cos 
falls on the ground at a distance of 2
90 m. If the ball is thrown with the u sin 
(c) (d) None of these
same initial velocity at an angle 30o, 2
it will fall on the ground at a 42. If two bodies are projected at 30o
distance of and 60o respectively, with the same
(a) 30 m (b) 60 m velocity, then
(c) 90 m (d) 120 m (a) Their ranges are same
37. Four bodies P, Q, R and S are (b) Their heights are same
projected with equal velocities (c) Their times of flight are same
having angles of projection 15o, 30o, (d) All of these
45o and 60o with the horizontal 43. A body is thrown with a velocity of
respectively. The body having 9.8 m/s making an angle of 30o with
shortest range is the horizontal. It will hit the ground
(a) P (b) Q after a time
(c) R (d) S (a) 1.5 s (b) 1 s
38. For a projectile, the ratio of (c) 3 s (d) 2 s
maximum height reached to the 44. A cricketer can throw a ball to a
square of flight time is maximum horizontal distance of
(g = 10 ms–2) 100 m. With the same effort, he
(a) 5 : 4 (b) 5 : 2 throws the ball vertically upwards.
(c) 5 : 1 (d) 10 : 1 The maximum height attained by
the ball is
39. Which of the following sets of (a) 100 m (b) 80 m
factors will affect the horizontal (c) 60 m (d) 50 m
distance covered by an athlete in a 45. A cricketer can throw a ball to a
long–jump event maximum horizontal distance of
(a) Speed before he jumps and his 100 m. The speed with which he
weight throws the ball is (to the nearest
(b) The direction in which he leaps integer)
and the initial speed (a) 30 ms–1 (b) 42ms–1
(c) The force with which he pushes (c) 32ms–1 (d) 35ms–1
the ground and his speed 46. A ball is projected with velocity Vo
(d) None of these at an angle of elevation 30°. Mark
40. A ball thrown by one player reaches the correct statement
the other in 2 sec. the maximum (a) Kinetic energy will be zero at the
highest point of the trajectory
PHYSICS-I PROJECTILE MOTION ENTRY -TEST 2023

(b) Vertical component of momentum horizontal range and the maximum

will be conserved height reached will be in the ratio.
(c) Horizontal component of (a) 1 : 2 (b) 2 : 1
momentum will be conserved (c) 1 : 4 (d) 4 : 1
(d) Gravitational potential energy will 52. The maximum horizontal range of a
be minimum at the highest projectile is 400 m. The maximum
point of the trajectory value of height attained by it will be
47. A stone is thrown at an angle  to
the horizontal reaches a maximum (a) 100 m (b) 200 m
height H. Then the time of flight of (c) 400 m (d) 800 m
stone will be 53. The net force acting in an inertial
2H 2H frame is:
(a) (b) 2
g g (a) Positive (b) Negative
2 2 H sin  2 H sin  (c) Zero (d) None of these
(c) (d) 54. Rockets use thrust forces which
g g
produces:
48. The horizontal range of a projectile
(a) Constant acceleration
is 4 3 times its maximum height. (b) Variable acceleration
Its angle of projection will be (c) Constant velocity
(a) 45 o (b) 60 o (d) Linearly varying velocity
(c) 90 o (d) 30 o 55. If a car is travelling eastward and
slowing down, what is the direction
49. Two bodies are thrown up at angles of acceleration?
of 45o and 60o, respectively, with the (a) Eastward
horizontal. If both bodies attain (b) Westward
same vertical height, then the ratio (c) neither eastward nor westward
of velocities with which these are (d) we can not answer with this data
thrown is
2
(a) (b) 2
3 3
3 3
(c) (d)
2 2
50. At what point of a projectile motion
acceleration and velocity are
perpendicular to each other
(a) At the point of projection
(b) At the point of drop
(c) At the topmost point
(d) Any where in between the point of
projection and topmost point
51. An object is projected at an angle of
45° with the horizontal. The
PHYSICS-I PROJECTILE MOTION ENTRY -TEST 2023

Answers Explanations 1
5 = (25 sin  )  2 −  10  (2)2
2

1. (b) 25 = 50 sin  sin  = 12   = 30 

2. (d) 16. (c) For angle (45  −  ) ,
3. (c) angle along vertical axis R=
u sin(90  − 2 ) u cos 2
2
=
2

v cos 
2 2 g g
h= For angle (45  +  ) ,
2g
u 2 sin(90  + 2 ) u 2 cos 2
4. (d) R= =
g g
5. (b) RTan = 4H max u 2 sin 2
17. (b) Range is given by R=
(c) H = u sin   H  u 2 . If initial velocity
2 2
6. g
2g g
On moon gm = . Hence Rm = 6 R
be doubled then maximum height 6
reached by the projectile will 18. (c) For greatest height  = 90°
quadrupled. u 2 sin 2 (90 ) u 2
H max = = = h (given)
7. (d) 2g 2g
u sin 2(45 ) u 2
2 2
8. (a) An external force by gravity is R max = = = 2h
g g
present throughout the motion so
19. (c) R = 4 H cot  , if R = 4H then
momentum will not be conserved.
cot  = 1   = 45 
2
2
9. (a) Range = u sin
g
; when  = 90  , R = 0 20. (b) E ' = E cos 2  = E cos 2 (45 ) =
E
2
i.e. the body will fall at the point of 21. (b)
projection after completing one 22. (b)
dimensional motion under gravity. 23. (d) Acceleration through out the
10. (c) R = 4 H cot  . projectile motion remains constant
When R = H then cot  = 1/4   = tan −1 (4) and equal to g.
11. (c) Because there is no accelerating or 24. (c)
retarding force available in horizontal 25. (c) Time of flight = 2 u sin =
motion. g
2  50  sin 30
12. (a) Direction of velocity is always = 5s
10
tangent to the path so at the top of
26. (b) Change in momentum = 2mu sin 
trajectory, it is in horizontal direction
= 2  0.5  98  sin 30 = 45 N-s
and acceleration due to gravity is
always in vertically downward 27. (d) R = 4 H cot  , if R= 3 H then cot  =
3

4
direction. It means angle between v  = 538 '

and g are perpendicular to each other. 28. (c) Became vertical downward
13. (d) R = 4 H cot  if  = 45  then displacement of both (barrel and
R = 4 H cot(45 ) = 4 H bullet) will be equal.
 sin 2 1 sin 2 30 

2 2
u 2 sin(2  15 ) u 2
14. (b) R15  = = = 1 .5 km 29. (b) As H = u sin H1
= = =
g 2g 2g H22
sin  2 sin 60
u sin(2  45 ) u
2 2 1/4
=
1
R45  = = = 1 . 5  2 = 3 km
g g 3/4 3
v 2 sin 2
15. (a) For vertical upward motion 30. (d) R=   = 12 sin −1  gR2 
1 g v 
h = ut − gt 2
2
PHYSICS-I PROJECTILE MOTION ENTRY -TEST 2023
2u sin  46. (c) Since horizontal component of
31. (a) T= = 10 sec  u sin  = 50 m/s
g
velocity is constant, hence momentum
sin 2  (u sin  )2 50  50
H = u
2
= = = 125 m is constant.
2g 2g 2  10
32. (b) For complementary angles range 47. (b) H =
u 2 sin 2 
and T = 2u sin  
2g g
will be equal. 4 u sin 
2 2
T2 =
(b) R = u sing 2 = (500 ) 10
 sin 30 
2 2
33. = 12 .5  10 3 m g2

 TH T =
2
8 8H 2H
2u sin  = =2
34. (a) T=  g g g
g
Tg 2  9 .8 48. (d) R = 4 H cot  , if R = 4 3H then cot  = 3
u= = = 19 . 6 m / s
2 sin  2  sin 30   = 30 
u 2 sin 2 2 2

35. (c) R= = R  u 2 . So if the speed of 49. (c) Hmax = u sin
g 2g
projection doubled, the range will According to problem
becomes four times, u1 sin 45  u 2 sin 60 
2
=
2 2 2

i.e., 4  50 = 200 m 2g 2g
sin 2 60 
2
u1 u 3 /2 3
36. (c) Range will be equal for  =  1 = = .
u2 2
sin 2 45  u2 1/ 2 2
complementary angles.
50. (c)
37. (a) When the angle of projection is
very far from 45° then range will be 51. (d) R = 4 H cot  , if  = 45  then R = 4 H 
R 4
minimum. =
H 1

(a) H = u sin  and T = 2u sin 

2 2
38. u2
2g g
52. (b) R m ax = = 400 m (For  = 45 )
g
H u 2 sin 2  / 2 g g 5 u2
So = = = H max = =
400
= 200 m (For  = 90 )
T 2
4 u sin  / g
2 2 2
8 4 2g 2
2
sin 2
39. (b) Range = u . It is clear that range
g
53. (c)
is proportional to the direction (angle) 54. (b)
and the initial speed. 55. (b)
40. (c) 2u sin  = 2 sec  u sin = 10
g
sin 2  100
H = u
2
= = 5m
2g 2g
41. (b) Only horizontal component of
velocity (u cos  ) .
42. (a) For complementary angles range is
same.
43. (b) T = 2u sin = 2  9.8  sin 30 = 1 s
g 9 .8
2
44. (d) Maximum range = ug = 100 m

2
Maximum height = u2 g = 100
2
= 50 m

45. (c) R m ax =
u2
g
= 100  u = 10 10 = 32 m / s
PHYSICS-I PROJECTILE MOTION ENTRY -TEST 2023