Motion in a Plane- 1 Practice Questions - DPP for NEET

 Page 1


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 The path followed by a body projected along y axis is given
by  y = 3 x – (1/2) x
2
.  If g = 10 m/s
2
 , then the initial
velocity of projectile will be – (x and y are in m)
(a) 3 10 m/s (b)2 10 m/s
(c) 10 3 m/s (d) 10 2 m/s
Q.2 When the angle of elevation of a gun are 60º and 30º
respectively , the height it shoots are h
1
 and h
2
 respectively ,
h
1
/h
2
 equal to –
(a) 3/1 (b) 1/3 (c) 1/2 (d) 2/1
Q.3 If t
1
 be the time taken by a body to clear the top of a building
and t
2
 be the  time spent in air, then t
2
 : t
1
 will be –
(a) 1 : 2 (b) 2 : 1 (c) 1 : 1 (d) 1 : 4
Q.4 The co-ordinates of a moving particle at any time t are given
by  x = ct
2
 and y = bt
2
. The speed of the particle is
(a) 2t (c + b) (b) 2t 
2 2
b c -
(c)t
2 2
b c +
(d) 2t
2 2
b c +
Q.5 The height y and the distance x along the horizontal at plane
of the projectile on a certain planet (with no surrounding
atmosphere) are given by y = (8t – 5t
2
) metre and x = 6t
metre where t is in second. The velocity with which the
projectile is projected is
(a) 8 m/s (b) 6 m/s
(c) 10 m/s (d) Data is insufficient
Page 2


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 The path followed by a body projected along y axis is given
by  y = 3 x – (1/2) x
2
.  If g = 10 m/s
2
 , then the initial
velocity of projectile will be – (x and y are in m)
(a) 3 10 m/s (b)2 10 m/s
(c) 10 3 m/s (d) 10 2 m/s
Q.2 When the angle of elevation of a gun are 60º and 30º
respectively , the height it shoots are h
1
 and h
2
 respectively ,
h
1
/h
2
 equal to –
(a) 3/1 (b) 1/3 (c) 1/2 (d) 2/1
Q.3 If t
1
 be the time taken by a body to clear the top of a building
and t
2
 be the  time spent in air, then t
2
 : t
1
 will be –
(a) 1 : 2 (b) 2 : 1 (c) 1 : 1 (d) 1 : 4
Q.4 The co-ordinates of a moving particle at any time t are given
by  x = ct
2
 and y = bt
2
. The speed of the particle is
(a) 2t (c + b) (b) 2t 
2 2
b c -
(c)t
2 2
b c +
(d) 2t
2 2
b c +
Q.5 The height y and the distance x along the horizontal at plane
of the projectile on a certain planet (with no surrounding
atmosphere) are given by y = (8t – 5t
2
) metre and x = 6t
metre where t is in second. The velocity with which the
projectile is projected is
(a) 8 m/s (b) 6 m/s
(c) 10 m/s (d) Data is insufficient
2
DPP/ P 06
Q.6 A body is thrown at an angle 30º to the horizontal with the
velocity of 30 m/s. After 1 sec, its velocity will be
(in m/s)   (g = 10 m/s
2
)
(a) 10 7 (b) 700 10 (c) 100 7 (d) 10
Q.7 A particle is moving in a plane with a velocity given by ,
u
r
 = u
0
 
i
ˆ
+ (wa cos wt) j
ˆ
, where i
ˆ
 and j
ˆ
 are unit vectors
along x and y-axes respectively . If the particle is at the origin
at t = 0, then  its distance from the origin at time  t = 3p/
2w will be
(a)
ú
ú
û
ù
ê
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
2
2
0
a
2
u 3
(b) ú
û
ù
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
2 0
a
2
u 3
(c)
ú
ú
û
ù
ê
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
a
2
u 3
2
0
(d)
ú
ú
û
ù
ê
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
2
2
0
a
2
u 4
Q.8 A ball thrown by one player reaches the other in 2 sec. The
maximum height attained by the ball above the point of
projection will be about-
(a) 2.5 m (b) 5 m (c) 7.5 m (d) 10 m
Q.9 Rishabh and Bappy are playing with two different balls of
masses m and 2m respectively. If Rishabh throws his ball
vertically up and Bappy at an angle q, both of them stay in
our view for the same period. The height attained by the
two balls are in the ratio of
(a) 2 : 1 (b) 1 : 1 (c) 1 : cos q (d) 1 : sec q
Q.10 A projectile is thrown at an angle q and (90
0
 – q) from the
same point with same velocity 98 m/s. The heights attained
by them, if the difference of heights is 50 m will be (in m)
(a) 270, 220 (b) 300, 250
(c) 250, 200 (d) 200, 150
Q.11 A particle is projected with a velocity u so  that its horizontal
range is twice the maximum height attained. The horizontal
range is
(a)u
2
/g (b) 2u
2
 /3g (c) 4u
2
/5g (d)u
2
/2g
Q.12 Mr C.P. Nawani kicked off a football with an initial speed
19.6 m/s at a projection angle 45º. A receiver on the goal
line 67.4 m away in the direction of the kick starts running
to meet the ball at that instant. What must be his speed so
that he could catch the ball before hitting the ground ?
(a) 2.82 m/s (b) 2/ 2 m/s
(c) 39.2 m/s (d) 10 m/s
Q.13 A ball is thrown from ground level so as to just clear a wall
4 metres high at  a distance of 4 metres and falls at a distance
of 14 metres from the wall. The magnitude of velocity of
the ball will be
(a)
182
 m/s (b) 
181
m/s
(c) 185 m/s (d) 186 m/s
Q.14 A ball is projeced from O with an initial velocity 700 cm/
s in a direction 37
°
 above the horizontal. A ball B, 500 cm
away from O on the line of the initial velocity of A, is
released  from rest at the instant A is projected. The height
through which B falls, before it is hit by A and  the direction
of the velocity A at the time of impact will respectively be
[given g = 10 m/s
2
, sin 37° = 0.6 and cos 37° = 8.0]
(a) 250 cm, 28° 42' (b) 255 cm, 27° 43'
(c) 245 cm, 20° 44' (d) 300 cm, 27° 43'
Q.15 A ball is thrown horizontally from a height of 20 m. It hits
the ground with a velocity three times its initial velocity.
The initial velocity of ball is
(a) 2 m/s (b) 3 m/s (c) 5 m/s (d) 7 m/s
Q.16 A projectile thrown from a height of 10 m with velocity of
2 m/s, the projectile will fall, from the foot of
projection, at distance-(g = 10 m/s
2
)
(a) 1 m (b) 2 m (c) 3m (d) 2 m
Q.17 Savita throws a ball horizontally with a velocity of 8 m/s
from the top of her building. The ball strikes to her brother
Sudhir playing at 12 m away from the building. What is the
height of the building ?
(a) 11m (b) 10 m (c) 8 m (d) 7 m
Q.18 A body is projected downdwards at an angle of 30º to the
horizontal with a velocity of 9.8 m/s from the top of a tower
29.4 m high. How long will it take before striking the
ground?
(a) 1s (b) 2s (c) 3s (d) 4s
Page 3


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 The path followed by a body projected along y axis is given
by  y = 3 x – (1/2) x
2
.  If g = 10 m/s
2
 , then the initial
velocity of projectile will be – (x and y are in m)
(a) 3 10 m/s (b)2 10 m/s
(c) 10 3 m/s (d) 10 2 m/s
Q.2 When the angle of elevation of a gun are 60º and 30º
respectively , the height it shoots are h
1
 and h
2
 respectively ,
h
1
/h
2
 equal to –
(a) 3/1 (b) 1/3 (c) 1/2 (d) 2/1
Q.3 If t
1
 be the time taken by a body to clear the top of a building
and t
2
 be the  time spent in air, then t
2
 : t
1
 will be –
(a) 1 : 2 (b) 2 : 1 (c) 1 : 1 (d) 1 : 4
Q.4 The co-ordinates of a moving particle at any time t are given
by  x = ct
2
 and y = bt
2
. The speed of the particle is
(a) 2t (c + b) (b) 2t 
2 2
b c -
(c)t
2 2
b c +
(d) 2t
2 2
b c +
Q.5 The height y and the distance x along the horizontal at plane
of the projectile on a certain planet (with no surrounding
atmosphere) are given by y = (8t – 5t
2
) metre and x = 6t
metre where t is in second. The velocity with which the
projectile is projected is
(a) 8 m/s (b) 6 m/s
(c) 10 m/s (d) Data is insufficient
2
DPP/ P 06
Q.6 A body is thrown at an angle 30º to the horizontal with the
velocity of 30 m/s. After 1 sec, its velocity will be
(in m/s)   (g = 10 m/s
2
)
(a) 10 7 (b) 700 10 (c) 100 7 (d) 10
Q.7 A particle is moving in a plane with a velocity given by ,
u
r
 = u
0
 
i
ˆ
+ (wa cos wt) j
ˆ
, where i
ˆ
 and j
ˆ
 are unit vectors
along x and y-axes respectively . If the particle is at the origin
at t = 0, then  its distance from the origin at time  t = 3p/
2w will be
(a)
ú
ú
û
ù
ê
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
2
2
0
a
2
u 3
(b) ú
û
ù
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
2 0
a
2
u 3
(c)
ú
ú
û
ù
ê
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
a
2
u 3
2
0
(d)
ú
ú
û
ù
ê
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
2
2
0
a
2
u 4
Q.8 A ball thrown by one player reaches the other in 2 sec. The
maximum height attained by the ball above the point of
projection will be about-
(a) 2.5 m (b) 5 m (c) 7.5 m (d) 10 m
Q.9 Rishabh and Bappy are playing with two different balls of
masses m and 2m respectively. If Rishabh throws his ball
vertically up and Bappy at an angle q, both of them stay in
our view for the same period. The height attained by the
two balls are in the ratio of
(a) 2 : 1 (b) 1 : 1 (c) 1 : cos q (d) 1 : sec q
Q.10 A projectile is thrown at an angle q and (90
0
 – q) from the
same point with same velocity 98 m/s. The heights attained
by them, if the difference of heights is 50 m will be (in m)
(a) 270, 220 (b) 300, 250
(c) 250, 200 (d) 200, 150
Q.11 A particle is projected with a velocity u so  that its horizontal
range is twice the maximum height attained. The horizontal
range is
(a)u
2
/g (b) 2u
2
 /3g (c) 4u
2
/5g (d)u
2
/2g
Q.12 Mr C.P. Nawani kicked off a football with an initial speed
19.6 m/s at a projection angle 45º. A receiver on the goal
line 67.4 m away in the direction of the kick starts running
to meet the ball at that instant. What must be his speed so
that he could catch the ball before hitting the ground ?
(a) 2.82 m/s (b) 2/ 2 m/s
(c) 39.2 m/s (d) 10 m/s
Q.13 A ball is thrown from ground level so as to just clear a wall
4 metres high at  a distance of 4 metres and falls at a distance
of 14 metres from the wall. The magnitude of velocity of
the ball will be
(a)
182
 m/s (b) 
181
m/s
(c) 185 m/s (d) 186 m/s
Q.14 A ball is projeced from O with an initial velocity 700 cm/
s in a direction 37
°
 above the horizontal. A ball B, 500 cm
away from O on the line of the initial velocity of A, is
released  from rest at the instant A is projected. The height
through which B falls, before it is hit by A and  the direction
of the velocity A at the time of impact will respectively be
[given g = 10 m/s
2
, sin 37° = 0.6 and cos 37° = 8.0]
(a) 250 cm, 28° 42' (b) 255 cm, 27° 43'
(c) 245 cm, 20° 44' (d) 300 cm, 27° 43'
Q.15 A ball is thrown horizontally from a height of 20 m. It hits
the ground with a velocity three times its initial velocity.
The initial velocity of ball is
(a) 2 m/s (b) 3 m/s (c) 5 m/s (d) 7 m/s
Q.16 A projectile thrown from a height of 10 m with velocity of
2 m/s, the projectile will fall, from the foot of
projection, at distance-(g = 10 m/s
2
)
(a) 1 m (b) 2 m (c) 3m (d) 2 m
Q.17 Savita throws a ball horizontally with a velocity of 8 m/s
from the top of her building. The ball strikes to her brother
Sudhir playing at 12 m away from the building. What is the
height of the building ?
(a) 11m (b) 10 m (c) 8 m (d) 7 m
Q.18 A body is projected downdwards at an angle of 30º to the
horizontal with a velocity of 9.8 m/s from the top of a tower
29.4 m high. How long will it take before striking the
ground?
(a) 1s (b) 2s (c) 3s (d) 4s
DPP/ P 06
3
Q.19 A ball is thrown from the top of a tower with an initial velocity
of 10 m/s at an angle of 30º above the horizontal. It hits the
ground at a distance of 17.3 m from the base of the tower.
The height of the tower (g = 10 m/s
2
) will be
(a) 1 0 m (b) 1 2 m (c) 110 m (d) 100 m
Q.20 A ball 'A' is projected from origin with an initial velocity
v
0
 = 700 cm/sec in a direction 37º above the horizontal as
shown in fig .Another ball 'B' 300 cm from origin on a line
37º above the horizontal is released from rest at the instant
A starts. How far will B have fallen when  it is hit by A ?
X O
B
A
y-axis
OB = 300 cm
Y
(a) 9 cm (b) 90 cm
(c) 0.9 cm (d) 900 cm
DIRECTIONS (Q.21-Q.23) : In the following questions,
more than one of the answers  given are correct. Select
the correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.21Choose the correct options
(1) A ball is dropped from the window of a moving train
on horizontal rails, the path followed by the ball as
observed by the observer on the ground is parabolic
path.
(2) If T be the total time of flight of a current of water
and H be the maximum height attained by it from the
point of projection, then H/T will be (1/4) u sinq
(u = projection velocity and q = projection angle)
(3) A hunter aims his gun and fires a bullet directly at a
monkey on a tree. At the instant bullet leaves the gun,
monkey drops, the bullet misses to hit the monkey.
(4) If a baseball player can throw a ball at  maximum
distance = d over a ground, the maximum vertical
height to which he can throw it, will be d
(Ball have same initial speed in each case)
Q.22A ball projected with speed 'u' at an angle of projection
15º has range R. The other angle of projection at which the
range will not be same with same initial speed 'u' is
(1) 45º (2) 35º
(3) 90º (4) 75º
Q.23 A projectile can have the same range R for two angles of
projections. If t
1
 and t
2
 be the times of flight in two cases,
then choose the incorrect relations –
(1) t
1
t
2
 µ 1/R
2
(2) t
1
t
2
 µ R
2
(3) t
1
t
2
 µ 1/R (4) t
1
t
2
 µ R
DIRECTIONS (Q.24-Q.26) : Read the passage given below
and answer the questions that follows :
Velocity at a general point P(x, y) for a horizontal projectile
motion is given by
v = 
2
y
2
x
v v + ;   tan a = 
x
y
v
v
      
R
h
u
u
gt
v=
2 2 2
t g u +
a is angle made by v with horizontal in clockwise direction
Trajectory equation for a horizontal projectile motion is given
by  x = v
x
t = ut
y = – (1/2) gt
2
      
v
y
v
x
v
a
eliminating t, we get y = – (1/2) 
2
2
u
gx
Page 4


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 The path followed by a body projected along y axis is given
by  y = 3 x – (1/2) x
2
.  If g = 10 m/s
2
 , then the initial
velocity of projectile will be – (x and y are in m)
(a) 3 10 m/s (b)2 10 m/s
(c) 10 3 m/s (d) 10 2 m/s
Q.2 When the angle of elevation of a gun are 60º and 30º
respectively , the height it shoots are h
1
 and h
2
 respectively ,
h
1
/h
2
 equal to –
(a) 3/1 (b) 1/3 (c) 1/2 (d) 2/1
Q.3 If t
1
 be the time taken by a body to clear the top of a building
and t
2
 be the  time spent in air, then t
2
 : t
1
 will be –
(a) 1 : 2 (b) 2 : 1 (c) 1 : 1 (d) 1 : 4
Q.4 The co-ordinates of a moving particle at any time t are given
by  x = ct
2
 and y = bt
2
. The speed of the particle is
(a) 2t (c + b) (b) 2t 
2 2
b c -
(c)t
2 2
b c +
(d) 2t
2 2
b c +
Q.5 The height y and the distance x along the horizontal at plane
of the projectile on a certain planet (with no surrounding
atmosphere) are given by y = (8t – 5t
2
) metre and x = 6t
metre where t is in second. The velocity with which the
projectile is projected is
(a) 8 m/s (b) 6 m/s
(c) 10 m/s (d) Data is insufficient
2
DPP/ P 06
Q.6 A body is thrown at an angle 30º to the horizontal with the
velocity of 30 m/s. After 1 sec, its velocity will be
(in m/s)   (g = 10 m/s
2
)
(a) 10 7 (b) 700 10 (c) 100 7 (d) 10
Q.7 A particle is moving in a plane with a velocity given by ,
u
r
 = u
0
 
i
ˆ
+ (wa cos wt) j
ˆ
, where i
ˆ
 and j
ˆ
 are unit vectors
along x and y-axes respectively . If the particle is at the origin
at t = 0, then  its distance from the origin at time  t = 3p/
2w will be
(a)
ú
ú
û
ù
ê
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
2
2
0
a
2
u 3
(b) ú
û
ù
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
2 0
a
2
u 3
(c)
ú
ú
û
ù
ê
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
a
2
u 3
2
0
(d)
ú
ú
û
ù
ê
ê
ë
é
+ ÷
ø
ö
ç
è
æ
w
p
2
2
0
a
2
u 4
Q.8 A ball thrown by one player reaches the other in 2 sec. The
maximum height attained by the ball above the point of
projection will be about-
(a) 2.5 m (b) 5 m (c) 7.5 m (d) 10 m
Q.9 Rishabh and Bappy are playing with two different balls of
masses m and 2m respectively. If Rishabh throws his ball
vertically up and Bappy at an angle q, both of them stay in
our view for the same period. The height attained by the
two balls are in the ratio of
(a) 2 : 1 (b) 1 : 1 (c) 1 : cos q (d) 1 : sec q
Q.10 A projectile is thrown at an angle q and (90
0
 – q) from the
same point with same velocity 98 m/s. The heights attained
by them, if the difference of heights is 50 m will be (in m)
(a) 270, 220 (b) 300, 250
(c) 250, 200 (d) 200, 150
Q.11 A particle is projected with a velocity u so  that its horizontal
range is twice the maximum height attained. The horizontal
range is
(a)u
2
/g (b) 2u
2
 /3g (c) 4u
2
/5g (d)u
2
/2g
Q.12 Mr C.P. Nawani kicked off a football with an initial speed
19.6 m/s at a projection angle 45º. A receiver on the goal
line 67.4 m away in the direction of the kick starts running
to meet the ball at that instant. What must be his speed so
that he could catch the ball before hitting the ground ?
(a) 2.82 m/s (b) 2/ 2 m/s
(c) 39.2 m/s (d) 10 m/s
Q.13 A ball is thrown from ground level so as to just clear a wall
4 metres high at  a distance of 4 metres and falls at a distance
of 14 metres from the wall. The magnitude of velocity of
the ball will be
(a)
182
 m/s (b) 
181
m/s
(c) 185 m/s (d) 186 m/s
Q.14 A ball is projeced from O with an initial velocity 700 cm/
s in a direction 37
°
 above the horizontal. A ball B, 500 cm
away from O on the line of the initial velocity of A, is
released  from rest at the instant A is projected. The height
through which B falls, before it is hit by A and  the direction
of the velocity A at the time of impact will respectively be
[given g = 10 m/s
2
, sin 37° = 0.6 and cos 37° = 8.0]
(a) 250 cm, 28° 42' (b) 255 cm, 27° 43'
(c) 245 cm, 20° 44' (d) 300 cm, 27° 43'
Q.15 A ball is thrown horizontally from a height of 20 m. It hits
the ground with a velocity three times its initial velocity.
The initial velocity of ball is
(a) 2 m/s (b) 3 m/s (c) 5 m/s (d) 7 m/s
Q.16 A projectile thrown from a height of 10 m with velocity of
2 m/s, the projectile will fall, from the foot of
projection, at distance-(g = 10 m/s
2
)
(a) 1 m (b) 2 m (c) 3m (d) 2 m
Q.17 Savita throws a ball horizontally with a velocity of 8 m/s
from the top of her building. The ball strikes to her brother
Sudhir playing at 12 m away from the building. What is the
height of the building ?
(a) 11m (b) 10 m (c) 8 m (d) 7 m
Q.18 A body is projected downdwards at an angle of 30º to the
horizontal with a velocity of 9.8 m/s from the top of a tower
29.4 m high. How long will it take before striking the
ground?
(a) 1s (b) 2s (c) 3s (d) 4s
DPP/ P 06
3
Q.19 A ball is thrown from the top of a tower with an initial velocity
of 10 m/s at an angle of 30º above the horizontal. It hits the
ground at a distance of 17.3 m from the base of the tower.
The height of the tower (g = 10 m/s
2
) will be
(a) 1 0 m (b) 1 2 m (c) 110 m (d) 100 m
Q.20 A ball 'A' is projected from origin with an initial velocity
v
0
 = 700 cm/sec in a direction 37º above the horizontal as
shown in fig .Another ball 'B' 300 cm from origin on a line
37º above the horizontal is released from rest at the instant
A starts. How far will B have fallen when  it is hit by A ?
X O
B
A
y-axis
OB = 300 cm
Y
(a) 9 cm (b) 90 cm
(c) 0.9 cm (d) 900 cm
DIRECTIONS (Q.21-Q.23) : In the following questions,
more than one of the answers  given are correct. Select
the correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.21Choose the correct options
(1) A ball is dropped from the window of a moving train
on horizontal rails, the path followed by the ball as
observed by the observer on the ground is parabolic
path.
(2) If T be the total time of flight of a current of water
and H be the maximum height attained by it from the
point of projection, then H/T will be (1/4) u sinq
(u = projection velocity and q = projection angle)
(3) A hunter aims his gun and fires a bullet directly at a
monkey on a tree. At the instant bullet leaves the gun,
monkey drops, the bullet misses to hit the monkey.
(4) If a baseball player can throw a ball at  maximum
distance = d over a ground, the maximum vertical
height to which he can throw it, will be d
(Ball have same initial speed in each case)
Q.22A ball projected with speed 'u' at an angle of projection
15º has range R. The other angle of projection at which the
range will not be same with same initial speed 'u' is
(1) 45º (2) 35º
(3) 90º (4) 75º
Q.23 A projectile can have the same range R for two angles of
projections. If t
1
 and t
2
 be the times of flight in two cases,
then choose the incorrect relations –
(1) t
1
t
2
 µ 1/R
2
(2) t
1
t
2
 µ R
2
(3) t
1
t
2
 µ 1/R (4) t
1
t
2
 µ R
DIRECTIONS (Q.24-Q.26) : Read the passage given below
and answer the questions that follows :
Velocity at a general point P(x, y) for a horizontal projectile
motion is given by
v = 
2
y
2
x
v v + ;   tan a = 
x
y
v
v
      
R
h
u
u
gt
v=
2 2 2
t g u +
a is angle made by v with horizontal in clockwise direction
Trajectory equation for a horizontal projectile motion is given
by  x = v
x
t = ut
y = – (1/2) gt
2
      
v
y
v
x
v
a
eliminating t, we get y = – (1/2) 
2
2
u
gx
4
DPP/ P 06
Q.24 A ball rolls off top of a stair way with a horizontal velocity
u m/s. If the steps are h m high and b meters wide, the ball
will just hit the edge of  n
th
 step if n equals to
(a)
2
2
gb
hu
(b)
2
2
gb
g u
(c)
2
2
gb
hu 2
(d)
2
2
hb
g u 2
Q.25 An aeroplane is in a level flying at an speed of 144 km/hr
at an altitude of 1000 m. How far horizontally from a given
target should a bomb be released from it to hit the target ?
(a) 571.43 m (b) 671.43 m
(c) 471.34 m (d) 371.34 m
Q.26 An aeroplane is flying horizontally with a velocity of 720
km/h at an altitude of 490 m. When it is just vertically above
the target a bomb is dropped from it. How far horizontally it
missed the target?
(a) 1000 m (b) 2000 m
(c) 100 m (d) 200 m
DIRECTIONS (Q.27-Q.28) : Each of these questions contains
two statements: Statement-1 (Assertion) and Statement-2
(Reason). Each of these questions has four alternative choices,
only one of which is the correct answer. You have to select
the correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.
Q.27 Statement -1 : Two projectiles are launched from the top
of a cliff with same initial speed with different angles of
projection. They reach the ground with the same speed.
Statement -2 : The work done by gravity is same in both the
cases.
Q.28 Statement-1 : A man projects a stone with speed u at some
angle. He again projects a stone with same speed such that
time of flight now is different. The horizontal ranges in
both the cases may be same. (Neglect air friction)
Statement-2 : The horizontal range is same for two
projectiles projected with same speed if one is projected
at an angle q with the horizontal and other is projected at
an angle (90° – q) with the horizontal. (Neglect air friction)