1. PART - I : OBJECTIVE QUESTIONS
Single choice type
1. A bomber plane moving at a horizontal speed of 20 m/s releases a bomb at a height of 80 m above
ground as shown. At the same instant a Hunter of negligible height starts running from a point below
it, to catch the bomb with speed 10 m/s. After two seconds he realized that he cannot make it, he
stops running and immediately holds his gun and fires in such direction so that just before bomb hits
the ground, bullet will hit it. What should be the firing speed of bullet. (Take g = 10 m/s2
)
80 m
Ground
10 m/s
20 m/s
(A) 10 m/s (B) 10
20 m/s (C) 10
10 m/s (D) None of these
2. A particle is projected from a point (0, 1) on Y-axis (assume + Y direction vertically upwards) aiming
towards a point (4, 9). It fell on ground on x axis in 1 sec.
Taking g = 10 m/s2
and all coordinate in metres. Find the X-coordinate where it fell.
(A) (3, 0) (B) (4, 0) (C) (2, 0) (D) ( 5
2 , 0)
3. Three stones A, B, C are projected from surface of very long inclined
plane with equal speeds and different angles of projection as shown
in figure. The incline makes an angle  with horizontal. If HA, HB and
HC are maximum height attained by A, B and C respectively above
inclined plane then : (Neglect air friction)
A
B
C
(A) HA + HC = HB (B) 2
B
2
C
2
A H
H
H 

(C) HA + HC = 2HB (D) 2
B
2
C
2
A H
2
H
H 

4. A ball is thrown from bottom of an incline plane at an angle  from the inclined surface up the plane.
Another ball is thrown from a point on the inclined plane with same speed and at same angle from
the inclined surface down the plane. If in the two cases, maximum height attained by the balls with
respect to the inclined surface during projectile motion are h1 and h2 then :
(A) h1 > h2 (B) h1 < h2
(C) h1 = h2 (D) All the three can be possible
5. A particle is projected from surface of the inclined plane with speed u and
at an angle  with the horizontal. After some time the particle collides
elastically with the smooth fixed inclined plane for the first time and
subsequently moves in vertical direction. Starting from projection, find the
time taken by the particle to reach maximum height. (Neglect time of
collision).
(A) g
cos
u
2 
(B) g
sin
u
2 
(C) g
)
cos
(sin
u 


(D) g
u
2

2. 6. Two stones A and B are projected from an inclined plane such that A has range up the incline and B
has range down the incline. For range of both stones on the incline to be equal in magnitude, pick up
the correct condition. (Neglect air friction)
A
B
(A) Component of initial velocity of both stones along the incline should be equal and also component
of initial velocity of both stones perpendicular to the incline should be equal.
(B) Horizontal component of initial velocity of both stones should be equal and also vertical
component of initial velocity of both stones should be equal.
(C) Component of initial velocity of both stones perpendicular to the incline should be equal and
also horizontal component of initial velocity of both stones should be equal in magnitude.
(D) None of these.
More than one choice type
7. A particle is projected from a point on the ground with an initial velocity of u = 50 m/s at an angle of 53°
with the horizontal (tan 53° = 4/3, g = 10 m/s2 = acceleration due to gravity).
(A) The velocity of the particle will make angle 45° with the horizontal after time 1 s.
(B) The velocity of the particle will make angle 45° with the horizontal after time 7 s.
(C) The average velocity between the point of projection and the highest point on its path is horizontal.
(D) The average velocity between two points on same height will be horizontal.
8. Two stones are projected from level ground. Trajectories of two stones are shown in figure. Both stones
have same maximum heights above level ground as shown. Let T1
and T2
be their time of flights and u1
and u2
be their speeds of projection respectively (neglect air resistance). Then
y
x
1 2
(A) T2
> T1
(B) T1
= T2
(C) u1
> u2
(D) u1
< u2
9. At the same instant, two boys throw balls A and B from the window with speeds 0
and k0
respectively,
where k is constant. They collide in air at time t. Which of the following options is/are correct.
(A) k =
1
2
cos
cos


(B) k =
1
2
sin
sin


(C) t =
)
sin
v
sin
kv
(
h
2
0
1
0 


(D) t =
)
cos
v
cos
kv
(
h
2
0
1
0 



3. PART - II : SUBJECTIVE QUESTIONS
1. Two ships A and B are stationary, facing away from each other. Ship A has a cannon at its back which fires
shell's with a speed of 10 m/s. Initially they are at a distance 5 3 m apart. Find the maximum and minimum
angle with which the shells should be projected from ship A to hit ship B. The ships are of equal length
 = 10  
2
5  m.
2. A projectile aimed at a mark which is in the horizontal plane through the point of projection falls a cm short
of it when the elevation is  and goes b cm too far when the elevation is . Show that if the velocity of
projection is same in all the case, the proper elevation is 










b
a
2
sin
a
2
sin
b
sin
2
1 1
3. A particle is thrown over a triangle from one end of a horizontal base and grazing the vertex falls on the other
end of the base. If  and  be the base angles and the angle of projection prove that tan  = tan  + tan .
4. Some students are playing cricket on the roof of a building of height 20 m. While playing, ball falls on the
ground. A person on the ground returns their ball with the minimum possible speed at angle 45° with the
horizontal. Find out the speed of projection.
5. A shell bursts on contact with the ground and pieces from it fly in all directions with all velocities upto 80 feet
per second. Show that a man 100 feet away is in danger for
2
5
seconds. [Use g = 32 ft/s2
].
6. A stone is thrown in such a manner that it would just hit a bird at the top of a tree and afterwards reach
a maximum height double that of the tree. If at the moment of throwing the stone the bird flies away
horizontally with constant velocity and the stone hits the bird after some time. Calculate the ratio of
horizontal velocity of stone to that of the bird.
7. A body is thrown from the surface of the Earth at an angle  to the horizontal with the initial velocity v0
.
v0
<< ve
ve
, (escape velocity of earth). Assuming the air drag to be negligible, find :
(a) the time of motion ;
(b) the maximum height of ascent and the horizontal range ; at what value of the angle  they will be equal
to each other ;
(c) the equation of trajectory y (x), where y and x are displacements of the body along the vertical
and the horizontal respectively ;
8. A cannon fires successively two shells with velocity v0
= 250 m/s; the first at the angle 1
 = 53° and the
second at the angle 2
 = 37° to the horizontal, in the same vertical plane, neglecting the air drag, find the
time interval between firings leading to the collision of the shells. (g = 10 m/s2
).
9. A stone is projected horizontally from a point P, so that it hits the inclined
plane perpendicularly. The inclination of the plane with the horizontal is 
and the point P is at a height h above the foot of the incline, as shown in
the figure. Determine the velocity of projection.
10. Two parallel straight lines are inclined to the horizontal at an angle . A particle is projected from a point mid
way between them so as to graze one of the lines and strikes the other at right angles. Show that if  is the
angle between the direction of projection and either of lines, then tan  =  
1
–
2 cot 
11. The benches of a gallery in a cricket stadium are 1 m high and 1 m wide. A batsman strikes the ball at
a level 1 m about the ground and hits a ball. The ball starts at 35 m/s at an angle of 53º with the
horizontal. The benches are perpendicular to the plane of motion and the first bench is 110 m from
the batsman. On which bench will the ball hit.
12. A ship is approaching a cliff of height 105 m above sea level. A gun fitted on the ship can fire shots
with a speed of 110 ms1
. Find the maximum distance from the foot of the cliff from where the gun can
hit an object on the top of the cliff. [ g = 10 m/s2
]

4. PART-I
1. (C) 2. (C) 3. (A) 4. (C) 5. (C) 6. (C)
7. (A), (B), (D) 8. (B), (D) 9. (A), (C)
PART-II
1. 30º & 60º 2. = 










b
a
2
sin
a
2
sin
b
sin
2
1 1
3. tan  = tan  + tan . 4. umin
= 2
20 m/s
5.
2
5
sec. 6.  
1
2  : 2
7. (a)  = 2 (v0
/ g) sin, (b) h = (v0
2
/ 2g)sin2
,  = (v0
2
/ g)sin2 ,  = 76º ;
(c) y= xtan – (g / 2v0
2
cos2
)x2
8. 10 s 9. v0
= 2
2gh
2 cot
 
10. tan  =  
1
–
2 cot  11. 6th step
12. 1100 m