Assignment-2: Projectile on inclined plane Date-01-06-2025

Q1. A shot fired with velocity v at an angle (+ ) to the horizontal hits the plane of angle 
sin  cos 
through the point of projection horizontally. Prove tan  
1  sin 2 

Q2. A ball starts falling with zero initial velocity on a smooth inclined plane forming an angle 
with the horizontal. Having fallen the distance h, the ball rebounds elastically off the
inclined plane. At what distance from the impact point will the ball rebound for the second
time? Also find the ratio of successive ranges of the ball along the plane.

Q3. A particle is projected from point A perpendicular to inclined

B
plane with a velocity 50 m/s as shown in the figure. Particle u
strikes a vertical plane perpendicularly at point B. Find the
time taken by particle in going from point A to point B. A

37

Q4. A projectile is thrown at an angle  with the horizontal with a velocity v on an inclined
plane making an angle  with the horizontal. The time when the velocity of the particle
becomes parallel to the incline is……………….. and the perpendicular distance of the
particle from the plane at this instant is……………………….

Q5. A stone is projected from the ground with a velocity 25 m/s. Two second latter, it just
crosses a wall 5 m high. Find (a) angle of the projection (b) the greatest height reached
(c) How the beyond wall the stone again hits the ground.

Q6. If the projectile takes a time t to reach from A to B is t, then the u B

distance AB is how much? The speed of projection is u.

60
30
A

Q7. The surface of a hill is inclined at an angle  to the horizontal. A stone is thrown from the
top of the hill at an angle  with the vertical with a velocity v0. How far from the top will the
stone strike the surface of the hill?

Q8. A stone is projected with a speed of 40 m/s at an angle of 40 m/s

300 with the horizontal from a tower of height 100 m above
0
30

ground. Find
( a) the maximum height attained by the stone.
( b) the horizontal distance from the tower where it hits the 100 m
ground.

Q9. A stone is projected from a tower of height ‘h’ as shown in O

figure. Find the speed with which it should be thrown, so
as to strike the incline plane normally. h

6
Q10. A particle projected with velocity v0 strikes at right angles a v0
plane passing through the point of projection and having
inclination  with the horizontal. Find the height (from horizontal 

plane) of the point where the particle strikes the plane v0 and .

Q11. Find the greatest distance that a stone can be thrown inside a horizontal tunnel 10 m
height with a velocity of projection 20 m/s. Also find the corresponding time of flight.

Q12. A stone is thrown with the velocity u = 20 m/s at an angle of  = 45 to the horizontal,
falls on the ground at the distance s from the point where it is thrown. From what height h
should the stone be thrown in a horizontal direction with the same initial velocity u for it to
2
fall at the same point?(g = 9.8 m/s )

Q13. Two bodies are projected from the same point with equal speeds and different angle of
projection. If they both strikes at the same point on an inclined plane whose inclination is
. If  be the angle of projection of the first body with the horizontal, then find the ratio of
their times of flights.

Q14. A batsman hits a ball at a height of 1.22 m above the ground so that ball leaves the bat
o
an angle 45 with the horizontal. A 7.31 m high wall is situated at a distance of 97.53 m
from the position of the batsman. Will the ball clear the wall if its range is 106.68m. Take
2
g = 10 m/s .

Q15. An aeroplane is flying in a horizontal direction with a velocity 600 km/hr at a height of
1960 m. When it is vertically above the point 'A' on the ground, a body is dropped from
it. The body strikes the ground at point B. Calculate the distance AB.

Q16. A man standing on a hill top projects a stone y

horizontally with speed v0 as shown in figure. Taking v0
(0, 0) x
the co-ordinate system as given in the figure, find the
co-ordinates of the point where the stone will hit the
hill surface.

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Answer : Assignment-2: Projectile on inclined plane
sin  cos 
Ans1. tan  =
1  sin2 
Ans2.  = 8 h sin 
Ans3. 4 sec
V sin(    V 2 sin2 (  
Ans4. ,
gcos  2gcos 
0 125 25 3
Ans5. ( a) 30 ( b) m ( c) m
16 4
ut
Ans6.
3
2v 20 cos      sin 
Ans7.
gcos2 
Ans8. ( a) 120m ( b) 238.9 m
2gh sin2 
Ans9.
1  sin2 
2v 20
Ans10.

g 4  cot 2  
Ans11. 40m
Ans12. 20 m
sin(  
Ans13.
cos 
Ans14. Yes, the ball will clear the wall
Ans15. 3300 m
 2v02 tan  2v02 tan 2  
Ans16.  , 
 g g 