MOTION IN A PLANE AND RELATIVE MOTION 121

EXERCISE – 3 : ADVANCED OBJECTIVE QUESTIONS

Single Choice Questions 7. A particle A is projected from the ground with an
1. There are two values of time for which a projectile is initial velocity of 10 m/s at an angle of 60° with
at the same height. The sum of these two times is horizontal. From what height h should another
equal to particle B be projected horizontally with velocity
(a) 3T/2 (b) 4T/3 5 m/s so that both the particles collide in ground at
(c) 3T/4 (d) T point C if both are projected simultaneously
(T = time of flight of the projectile) (g = 10 m/s2)
2. The trajectory of a projectile in a vertical plane is B 5 m/s
y = ax – bx2, where a and b are constants and x and y
are respectively horizontal and vertical distance of
h
the projectile from the point of projection. The 10 m/s
maximum height attained by the particle and the 60°
angle of projection from the horizontal are A C

b2
a2 (a) 10 m (b) 30 m
(a) , tan −1 ( b ) (b) , tan −1 ( 2a )
2a b (c) 15 m (d) 25 m
a 2
2a 2 8. A particle is projected at an angle of 60° above the
(c) , tan −1 ( a ) (d) , tan −1 ( a ) horizontal with a speed of 10 m/s. After some time
4b b
the direction of its velocity makes an angle of 30°
3. A particle moves in the x-y plane according to the
above the horizontal. The speed of the particle at this
law x = kt and y =kt (1 – at), where k and a are
instant is
positive constants and t is time. What is the equation
of trajectory of the particle? 5
(a) m/s (b) 5 3 m / s
αx 2 3
(a) y = kx (b) y = x −
k 10
(c) 5 m/s (d) m/s
αx 2 3
(c) y = (d) y = αx
k 9. In projectile motion, the modulus of rate of change
4. The equation of motion of a projectile is of speed
3 (a) is constant
y = 12x − x 2 . Given that g =10 ms–2, what is the
4 (b) first increases then decreases
range of the projectile
(c) first decreases then increases
(a) 12.4 m (b) 16 m
(d) none of these
(c) 30.6 m (d) 36.0 m
5. A ball is dropped from the top of a tower in a high- 10. Two particles A and B are projected simultaneously
speed wind. The wind exerts a steady force on the from a point situated on a horizontal plane. The
ball. The path followed by the ball will be particle A is projected vertically up with a velocity
(a) Parabola (b) Circular arc uA while the particle B is projected up at an angle of
(c) Elliptical arc (d) Straight line 30° with horizontal with a velocity uB. After 5 sec
6. A particle is projected from the ground with an the particles were observed moving mutually
initial speed of u at an angle θ with horizontal. The perpendicular to each other. The velocity of
average velocity of the particle between its point of projection of the particle uA and uB respectively are
projection and highest point of trajectory is (a) 50 ms–1, 100 m/s
u u (b) 100 ms–1, 50 ms–1
(a) 1 + 2 cos 2 θ (b) 1 + cos 2 θ
2 2 (c) uA > 25 m/s and uB <50 m/s
u (d) none of these
(c) 1 + 3cos 2 θ (d) u cos θ
2
MOTION IN A PLANE AND RELATIVE MOTION 122

11. A projectile is fired at an angle of 30° to the 16. A projectile is thrown in the upward direction
horizontal such that the vertical component of its making an angle of 60° with the horizontal
initial velocity is 80 m/s. Its time of flight is T. Its direction with a velocity of 147 ms–1. Then the time
velocity at t = T/4 has a magnitude of nearly after which its inclination with the horizontal is 45°
(a) 200 m/s (b) 300 m/s is
(c) 140 m/s (d) 100 m/s (a) 15 s (b) 10.98 s
12. A particle A is projected vertically upwards. (c) 5.49 s (d) 2.745 s
Another particle B of same mass is projected at an
17. From the top of a tower of height 40 m a ball is
angle of 45°. Both reach the same height. The ratio
projected upwards with a speed of 20 m/s at an
of the initial kinetic energy of A to that of B is
angle of elevation of 30o. Then the ratio of the total
1 time taken by the ball to hit the ground to its time of
[given KE = mv 2 ]
2 flight (time taken to come back to the same
(a) 1:2 (b) 2:1 elevation) is (take g = 10 ms2)
(c) 1 : 2 (d) 2 :1 (a) 2:1 (b) 3:1
13. A body of mass m is thrown upwards at an angle θ (c) 3:2 (d) 4:1
with the horizontal with velocity v. While rising up 18. Three identical balls are thrown with same speed at
the velocity of the mass after t seconds will be angles of 15°, 45° and 75° with the horizontal
(a) (v cos θ) 2 + (v sin θ) 2 respectively. The ratio of their distances from the
point of projection to the point where they hit the
(b) (v cos θ − v sin θ) 2 − gt ground will be

(c) v 2 + g 2 t 2 − (2 v sin θ) gt (a) 1: 2 :1 (b) 1 : 2 : 1

(c) 2 : 4 : 3 (d) 1: 2 : 3
(d) v 2 + g 2 t 2 − (2 v cos θ) gt
19. A projectile is thrown at an angle of 40° with the
14. From the top of a tower 19.6 m high, a ball is horizontal and its range is R1. Another projectile is
thrown horizontally. If the line joining the point of
thrown at an angle 40° with the vertical and its range
projection to the point where it hits the ground
is R2. What is the relation between R1 and R2?
makes an angle of 45° with the horizontal, then the
initial velocity of the ball is (a) R1 = R2 (b) R1 = 2 R2
(a) 9.8 ms–1 (b) 4.9 ms–1 (c) R2 = 2 R1 (d) R1 = 4 R2/5
(c) 14.7 ms–1 (d) 2.8 ms–1 20. A cricketer hits a ball with a velocity 25 m/s at 60°
15. A particle is projected with a speed V from a point above the horizontal. How far (approximately)
O making an angle of 30° with the vertical. At the above the ground it passes over a fielder 50 m from
same instant, a second particle is thrown vertically the bat (assume the ball is struck very close to the
upwards with a velocity v from a point A. The two ground)
particles reach H, the highest point on the parabolic (a) 8.2 m (b) 9.0 m
V
path of particle simultaneously. Then ratio is (c) 11.6 m (d) 12.7 m
v
21. From a point on the ground at a distance 2 metres
from the foot of a vertical wall, a ball is thrown at an
angle of 45° which just clears the top of the wall and
afterward strikes the ground at a distance 4m on the
other side. The height of the wall is
2 3
(a) m (b) m
3 4
1 4
(a) 3 2 (b) 2 3 (c) m (d) m
3 3
2 3
(c) (d)
3 2
MOTION IN A PLANE AND RELATIVE MOTION 123

22. Two projectiles A and B are projected with same 28. A body is projected at an angle of 30° with the
speed and angle of projection 30° for the projectile horizontal with speed 30 m/s. What is the angle with
A and 45° for the projectile B. If RA and RB are the the horizontal after 1.5 seconds? Take g = 10 m/s2.
horizontal ranges for the two projectiles, then (a) 0° (b) 30°
(a) RA = RB (c) 60° (d) 90°
(b) RA > RB 29. From certain height, two bodies are projected
horizontally with velocities 10 m/s and 20 m/s. They
(c) RA < RB
hit the ground in t1 and t2 seconds. Then
(d) the information is insufficient to decide the
(a) t1 = t2 (b) t1 = 2 t2
relation of RA and RB
23. A projectile is projected at an angle of 15° to the (c) t2 = 2 t1 (d) t1 = 2 t 2
horizontal with some speed v. If another projectile is 30. A body is projected with velocity v1 from the point
projected with the same speed, then it must be
A as shown in figure. At the same time, another
projected at what angle (other than 15°) with the
body is projected vertically upwards from B with
horizontal so as to have the same range.
velocity v2. The point B lies vertically below the
(a) It is never possible (b) 12.5°
v2
(c) 75° (d) 65° highest point. For both the bodies to collide,
v1
24. A fielder in a cricket match throws a ball from the
should be
boundary line to the wicket keeper. The ball
describes a parabolic path. Which of the following
quantities remains constant during the ball’s motion
in air? (neglect air resistance)
(a) its kinetic energy
(b) its speed
(c) the horizontal component of its velocity (a) 2 (b) 0.5
(d) the vertical component of its velocity (c) 3/ 2 (d) 1
25. The height y and the distance x along the horizontal 31. An aeroplane is flying at a constant horizontal
plane of a projectile on a certain planet (with no velocity of 600 km/h at an elevation of 6 km
surrounding atmosphere) are given by y = (8t – 5) towards a point directly above the target on the
metre and x = 6t metre where t is in seconds. The earth’s surface. At an appropriate time, the pilot
velocity of projection is released a ball so that it strikes the target on the
(a) 8 m/sec earth. The ball will appear to be falling
(b) 6 m/sec (a) on a parabolic path as seen by pilot in the plane
(c) 10 m/sec (b) vertically along a straight path as seen by an
(d) not obtained from the data observer on the ground near the target
26. A body is projected horizontally with speed 20 m/s (c) on a parabolic path as seen by an observer on the
from top of a tower. What will be its speed nearly ground near the target
after 5 sec? Take g = 10 m/s2 (d) on a zig-zag path as seen by pilot in the plane
(a) 54 m/s (b) 20 m/s 32. Three particles A, B and C are thrown from the top
(c) 50 m/s (d) 70 m/s of a tower 100 m in height with the same speed
10 m/s. A is thrown straight up, B is thrown straight
27. A body is projected horizontally with speed 20 m/s
down, and C is thrown horizontally. They hit the
from top of a tower, what will be the displacement
ground with the speeds vA, vB and vC respectively.
of the body if it hits the ground after 5 sec and
doesn’t bounce (quote nearest integer) Then
(a) 100 m (b) 125 m (a) vA > vB = vC (b) vB > vC > vA
(c) 160 m (d) 225 m (c) vA = vB = vC (d) vA = vB > vC
MOTION IN A PLANE AND RELATIVE MOTION 124

33. A body is thrown horizontally with a velocity 39. A particle P is projected from a point on the surface
2 gh from the top of a tower of height h. It strikes of smooth inclined plane (see figure).
Simultaneously another particle Q is released on the
the level ground through the foot of the tower at a
smooth inclined plane from the same position. P and
distance x from the tower. The value of x is
Q collide on the inclined plane after t = 4 second.
(a) h (b) h/2 The speed of projection of P is nearly:
(c) 2h (d) 2h/3
34. Consider a boy on a trolley who throws a ball with
speed 20 m/s with respect to ground at an angle 37°
with vertical and trolley is moving with a speed
10 m/s in horizontal direction then what will be
maximum distance travelled by ball parallel to road :
(a) 20.2 m (b) 12 m (a) 5 m/s (b) 10 m/s
(c) 31.2 m (d) 62.4 m (c) 15 m/s (d) 20 m/s
35. Two men A and B, A standing on the extended floor 40. A ball is projected horizontally with a speed v from
nearby a building and B is standing on the roof of the top of a plane inclined at an angle 45° with the
the building. Both throw a stone towards each other. horizontal. How far from the point of projection will
Then which of the following will be correct. the ball strike the plane?
(a) stone will hit A, but not B
v2 v2
(b) stone will hit B, but not A (a) (b) 2
g g
(c) stone will not hit either of them, but will collide
with each other 2 v2  2 v2 
(c) (d) 2  
(d) none of these
g  g 
36. A particle is projected from a point (0, 1) on Y–axis 41. Position vector of a particle moving in x-y plane at

(assume + Y direction vertically upwards) aiming time t is: r = a (1 − cos ωt ) ˆi + a sin ωt ˆj. The path of
towards a point (4, 9). It fell on ground along x axis the particle is
in 1 sec.
(a) a circle of radius a and centre at (a, 0)
Taking g = 10 m/s2 and all coordinate in metres.
(b) a circle of radius a and centre at (0, 0)
Find the x–coordinate of the point where it fell.
(c) an ellipse
(a) 3 (b) 4
(d) neither a circle nor an ellipse
(c) 2 (d) 2 5
42. A particle moves in x-y plane. The position vector
37. The position vector of a particle is given as


{ }
of particle at any time t is r = ( 2t ) ˆi + ( 2t 2 ) ˆj m.
( ) ( )
r = t 2 − 4t + 6 ˆi + t 2 ˆj. The time after which the
The rate of change of θ at time t = 2 second. (where
velocity vector and acceleration vector becomes θ is the angle which its velocity vector makes with
perpendicular to each other is equal to positive x-axis) is
(a) 1 sec (b) 2 sec
2 1
(c) 1.5 sec (d) not possible (a) rad / s (b) rad / s
17 14
38. A particle is projected up an inclined plane with
4 6
initial speed v = 20 m/s at an angle θ = 30o with (c) rad / s (d) rad / s
7 5
plane. The component of its velocity perpendicular
43. A particle has an initial velocity of 3iˆ + 4 ˆj and an
to plane when it strikes the plane is
acceleration of 0.4 ˆi + 0.3 ˆj . Its speed after 10 s is:
(a) 10 3 m / s (b) 10 m/s
(a) 10 unit (b) 7 unit
(c) 5 3 m / s (d) data is insufficient
(c) 7 2 unit (d) 8.5 unit
MOTION IN A PLANE AND RELATIVE MOTION 125

44. Velocity and acceleration of a particle initially are u2 1

(a) 1 − (b)

( )
v = 3iˆ + 4 ˆj m/s and

( )
a = − 6 ˆi + 8 ˆj m/s2 v2 u2
1− 2
respectively. Initially particle is at origin. maximum v
x–coordinate of particle will be: u2 1
(c) 1 + (d)
(a) 1.5 m (b) 0.75 m v2 u2
1+ 2
(c) 2.25 m (d) 4.0 m v
  50. A river is flowing from West to East at a speed of
45. Let v and a denote the velocity and acceleration
respectively of a particle moving in a circular path 5 metres per minute. A man on the south bank of the
then, river, capable of swimming at 10 metres per minute
  in still water, wants to swim across the river in
(a) v . a < 0 all the time shortest time. He should swim in a direction
 
(b) v . a > 0 all the time (a) due North (b) 30° East of North
  (c) 30° West of North (d) 60° East of North
(c) v . a = 0 all the time
(d) (a),(b) & (c) all are possible depending upon the 51. A river is flowing from west to east at a speed of
direction of net acceleration. 20 m/min. A man on the south bank of the river,
capable of swimming at 10 m/min in still water,
46. A person walks up a stationary escalator in time t1. If
wants to swim across the river without any drift. He
he remains stationary on the moving escalator, then should swim in a direction:
it can take him up in time t2. How much time would
(a) due north
it take him to walk up the moving escalator.
(b) 30° east of north
t +t
(a) 1 2 (b) t1 + t 2 (c) 30° west of north
2
(d) zero drift is not possible
t t
(c) 1 2 (d) t1 + t 2 52. The rowing speed of a man relative to water is
t1 + t 2 5 km/h and the speed of water flow is 3 km/h. At
47. A horizontal wind is blowing with a velocity v what angle to the river flow should he head if he
towards north-east. A man starts running towards wants to reach a point on the other bank, directly
north with acceleration a. The time after which man opposite to starting point:
will feel the wind blowing towards east is : (a) 127° (b) 143°
v 2v (c) 120° (d) 150°
(a) (b)
a a 53. Two cars are moving in the same direction with the
same speed of 30 km/h. They are separated by 5 km.
v 2v
(c) (d) What is the speed of the car moving in the opposite
2a a
direction if it meets the two cars at an interval of
48. Two trains are each 50 m long starts moving parallel 4 minutes?
towards each other at speeds 10 m/s and 15 m/s (a) 15 km/h (b) 30 km/h
respectively, after how much time will they pass
(c) 45 km/h (d) 60 km/h
each other?
(a) 8s (b) 4s
Multiple Choice Questions
(c) 2s (d) 6s
54. An observer moves with a constant speed along the
49. On a calm day a boat can go across a lake and return line joining two stationary objects. He will observe
in time T0 at a speed v. On a rough day there is that the two objects.
uniform current at speed u to help the onward (a) have the same speed
journey and impede the return journey. If the time (b) have the same velocity
taken to go across and return on the rough day be T,
(c) move in the same direction
then T/T0 is:
(d) move in opposite direction
MOTION IN A PLANE AND RELATIVE MOTION 126

55. A particle is projected at an angle θ from ground (a) the particles will collide the plane with same
with speed u (g = 10 m/s2) speed
(a) if u = 10 m/s and θ = 30°, then time of flight (b) the times of flight of each particle are same
will be 1 sec. (c) both particles strike the plane perpendicularly
(b) if u = 10 3 m/s and θ = 60°, then time of flight (d) the particles will collide in mid-air if projected
will be 3 sec. simultaneously and time of flight of each particle
(c) if u = 10 3 m/s and θ = 60°, then after 2 sec is less than the time of collision.
velocity becomes perpendicular to initial 59. Choose the correct alternative(s)
velocity. (a) If the greatest height to which a man can throw a
(d) if u = 10 m/s and θ = 30°, then velocity never stone is h, then the greatest horizontal distance
becomes perpendicular to initial velocity during up to which he can throw the stone is 2h
its flight. (b) The angle of projection for a projectile motion
56. A particle leaves the origin with an initial velocity whose range R is n times the maximum height H

( )
u = 3iˆ m/s and a constant acceleration is tan–1 (4/n)

( ) 
a = −1.0 ˆi − 0.5 ˆj m/s2. its velocity v and position
(c) The time-of-flight T and the horizontal range R
of a projectile are connected by the equation

vector r when it reaches its maximum x-co- gT2 = 2R tan θ where θ is the angle of
ordinate are: projection

(a) v = −2ˆj

( )
(b) v = −1.5jˆ m / s (d) A ball is thrown vertically up. Another ball is
thrown at an angle θ with the vertical. Both of

( )
(c) r = 4.5iˆ − 2.25jˆ m (d) r = ( 3iˆ − 2ˆj) m

them remain in air for the same period of time.
Then the ratio of heights attained by the two balls
57. In a projectile motion let tOA = t1 and tAB = t2. the
is 1 : 1.
horizontal displacement from O to A is R1 and from
60. Two particles A and B are located in x-y plane at
A to B is R2. Maximum height is H and time of
points (0, 0) and (0, 4 m). They simultaneously start
flight is T. If air drag is to be considered, then
moving with velocities.
choose the correct alternative (s)
 
y v A = 2ˆj m/s and v B = 2iˆ m/s. Select the correct
A alternative(s)
(a) the distance between them is constant
H
B (b) the distance between them first decreases and
x
O then increases
R1 R2
(c) the shortest distance between them is 2 2 m
(a) t1 will decrease while t2 will increase
(d) time after which they are at minimum distance is
(b) H will increase
1s
(c) R1 will decrease while R2 will increase
61. The co-ordinate of the particle in x-y plane are given
(d) T may increase or decrease
as x = 2 + 2t + 4t2 and y = 4t + 8t2 the motion of the
58. From an inclined plane two particles are projected particle is
with same speed at same angle θ , one up and other
(a) along a straight line
down the plane as shown in figure. Which of the
following statement(s) is/are correct? (b) uniformly accelerated
(c) along a parabolic path
(d) nonuniformly accelerated
MOTION IN A PLANE AND RELATIVE MOTION 127


62. River is flowing with a velocity v R = 4iˆ m/s. A boat Assertion & Reason

( )
is moving with a velocity v BR = −2iˆ + 4ˆj of m/s (A) If both Assertion and reason are true and reason is
the correct explanation of the assertion.
relative to river. The width of the river is 100 m
(B) If both assertion and reason are true but reason is not
along y-direction. Choose the correct alternative(s)
the correct explanation of the assertion.
(a) the boatman will cross the river in 25 s
(C) If assertion is true but reason is false.
(b) absolute velocity of boatman is 2 5 m/s
(D) If assertion is false but reason is true.
(c) drift of the boatman along the river current is 50
(E) If both assertion and reason are false.
m
(d) the boatman can never cross the river
68. Assertion: For a particle moving along a straight
line or in a plane, the average velocity vector over a
Numerical Value Type Questions
time interval can be equal to instantaneous velocity
63. A particle of mass m = 2 kg is projected along X–
–1
at the end of the interval, even if velocity of particle
axis with velocity V0 = 5 ms . It is acted on by a is not constant.
variable force acting along Y–axis as shown in   
r −r dr
figure. What is the magnitude of its velocity at 2 Reason: 2 1 =
–1 t 2 − t1 d t
seconds? (in ms )
(a) A (b) B
(c) C (d) D
(e) E
69. Assertion: Two stones are simultaneously projected
from level ground from same point with same
speeds but different angles with horizontal. Both
stones move in same vertical plane. Then the two
64. A man standing on a road has to hold his umbrella at
stones may collide in mid-air.
37° with the vertical to keep the rain away. He
throws the umbrella and starts running at 12 km/h. Reason: For two stones projected simultaneously
He finds that raindrops are hitting his head from same point with same speed at different angles
vertically. Find the speed (in km/hr) of raindrops with horizontal, their trajectories may intersect at
with respect to the moving man. some point.
 
65. ( ) ( )
VA = x ˆi + 2 ˆj m/s and VB = 3iˆ + 2 ˆj m/s find x
(a) A (b) B
(c) C (d) D
such that, the relative speed of A with respect to B
becomes 5 m/s. (e) E
66. A particle is projected up an inclined plane of 70. Assertion: In a plane to plane projectile motion, the
inclination β at an elevation α to the horizontal. angle between instantaneous velocity vector and
Find the ratio between tan α and tan β , if the acceleration vector can be anything between 0 to π
particle strikes the plane horizontally. (excluding the limiting case).

67. A train takes 2 minutes to acquire its full speed 60 Reason: In plane to plane projectile motion,
kmph from rest and 1 minute to come to rest from acceleration vector is always pointing vertical
the full speed. If somewhere in between two stations downwards. (neglect air friction).
1 km of the track be under repair and the limited (a) A (b) B
speed on this part be fixed to 20 kmph, find the late
(c) C (d) D
running of the train ( in sec) on account of this repair
work, assuming otherwise normal at running of the (e) E
train between the stations.
MOTION IN A PLANE AND RELATIVE MOTION 128

71. Assertion: Two particles of different mass, Paragraph Type Questions

projected with same velocity and angle of Using the following Comprehension, Solve Q. 75 to Q. 78
projection, the maximum height attained by both the Passage
particle will be same.
We know how by neglecting the air resistance, the
Reason: The maximum height of projectile is problems of projectile motion can be easily solved
independent of particle mass. and analysed. Now we consider the case of the
(a) A (b) B collision of a ball with a wall. In this case the
(c) C (d) D problem of collision can be simplified by
(e) E considering the case of elastic collision only. When
a ball collides with a wall, we can divide its velocity
72. Assertion: When a body is dropped or thrown
into two components, one perpendicular to the wall
horizontally from the same height, it would reach
and other parallel to the wall. If the collision is
the ground at the same time.
elastic, then the perpendicular component of
Reason: Horizontal velocity has no effect on the velocity of the ball gets reversed with the same
vertical direction. magnitude.
(a) A (b) B Vcos Vcos
(c) C (d) D
(e) E v Vsin Vsin
73. Assertion: In order to hit a target, a man should
point his rifle in the same direction as target. Velocity just Components of velocity Components of velocity
before collision just before collision just after collision
Reason: The horizontal range of the bullet is
independent of the angle of projection with The other parallel component of velocity will remain
horizontal. constant if wall is given smooth.
(a) A (b) B Now let us take a problem. Three balls ‘A’ and ‘B’
(c) C (d) D & ‘C’ are projected from ground with same speed at
same angle with the horizontal. The balls A, B and
(e) E
C collide with the wall during their flight in air and
all three collide perpendicularly with the wall as
Match the Column shown in figure.
74. A ball is projected from the ground with velocity v
such that its range is maximum. A C
B
Column–I Column–II
(A) Velocity at half of the (P) 3 v/2 75. Which of the following relation about the maximum
maximum height height H of the three balls from the ground during
their motion in air is correct:
v
(B) Velocity at the maximum (Q) (a) HA = HC > HB (b) HA > HB = HC
2
(c) HA > HC > HB (d) HA = HB = HC
height
76. If the time taken by the ball A to fall back on ground
(C) Change in its velocity when (R) v 2
is 4 seconds and that by ball B is 2 seconds. Then
it returns to the ground the time taken by the ball C to reach the inclined
v 5 plane after projection will be:
(D) Average velocity when it (S)
2 2 (a) 6 sec (b) 4 sec
reaches the maximum height (c) 3 sec (d) 5 sec
MOTION IN A PLANE AND RELATIVE MOTION 129

77. The maximum height attained by ball ‘A’ from the Paragraph Type Questions
ground is Using the following comprehension, solve Q. 79 & 80
(a) 10 m Passage
(b) 15 m An aircraft moving with a speed of 250 m/s is at a
(c) 20 m height of 6000 m, just overhead of an anti-aircraft
gun.
(d) insufficient information
79. If the muzzle velocity of the shell is 500 m/s, the
78. The maximum height attained by ball B from
firing angle θ should be
ground is:
(a) 20 m (b) 5 m
(c) 15 m (d) none of these

(a) 30o (b) 45o

o
(c) 60 (d) None of these
80. The time after which the aircraft is hit is:
(a) 20 3 s (b) 15 3 s

(c) 20 s (d) 10 3 s