PROJECTILE MOTION
1. Find the
angle of projection of a projectile for which the horizontal range and maximum
height are equal.
2. Prove that
the maximum horizontal range is four times the maximum height attained by the
projectile, when fired at an inclination so as to have maximum horizontal
range.
3. Show that
there are two values of time for which a projectile is at the same height. Also
show mathematically that the sum of these two times is equal to the time of
flight.
4. There are
two angle of projection for which the horizontal range is same. Show that the
sum of the maximum height for these two angles is independent of the angle of
projection.
5. A particle
is projected from ground with velocity 20√2 m/s at 45ᵒ. At what time particle is at the height of 15m from
the ground. (g=10 m/s2)
6. A particle
is projected from horizontal making an angle 60ᵒ
with initial velocity 40 m/s. Find the
time taken by the projectile to make angle 45ᵒ
from the horizontal.
7. A particle
is projected from the ground with initial velocity u=20√2 m/s at Ɵ=45ᵒ. Find:
a) R, H and T.
b) Velocity of projectile after 1 sec.
c) Velocity of particle at the time of
collision with the ground.
8. A projectile is fired horizontally
with a velocity of 98 m/s from the top of a hill 490 m high. Find:
a) The time taken by the projectile to
reach the ground.
b) The distance of the point where the
particle hit the ground foot of the hill.
c) The velocity with which the
projectile hits the ground. (g=10 ms-2)
9. A body is thrown horizontally from
the top of the tower and strikes the ground after three seconds at an angle of
45ᵒ with horizontal. Find the height of the tower and the speed with which the
body is projected. Take g =9.8 ms-2
10. A body is projected at an angle of
60ᵒ with horizontal with a speed of v= 20 m/s. taking g=10 ms-2.
Find the time after which the speed of the particle remains half of its initial
speed.
11. A ball rolls off the edge of the
horizontal table top 4 m high. If its strikes the floor at a point 5 m
horizontally away from the edge of the table, what was its speed at the instant
it left the table?
12. A particle moves in the plane xy
with constant acceleration a directed along the negative y-axis. The equation
of the motion of the particle has the form y=px-qx2 where p and q
are positive constants. Find the velocity of the particle at the origin of the
co-ordinates.
13. A ball is thrown from the ground
to clear the wall 3 m high at a distance of 6 m and falls 18 m away from the
wall. Find the angle of projection of the ball.
14. A particle moves in the xy-plane
with constant acceleration a directed along the negative y-axis. The equation
of the path of the particle has the form y=bx-cx2, where b and c are
positive constants. Find the velocity of the particle at the origin of
co-ordinates.
15. Two bodies are thrown with the
same initial velocity at angles Ɵ and (90-Ɵ) respectively with the horizontal,
then their maximum height are in the ratio.
16. A ball is thrown upwards with the
initial velocity v=15 m/s at an angle of 30ᵒ with the horizontal. The thrower
stands near the top of a long hill which slopes downwards at an angle of 20ᵒ.
When does the ball strikes the slope.
17. A body is projected horizontally
from the top of a tower with an initial velocity 18 m/s. It hits the ground at
an angle of 45ᵒ. What is the vertical component of the velocity when it strikes
the ground?
18. A particle is projected from the
ground with an initial velocity of 20 m/s at an angle of 30ᵒ with horizontal.
The magnitude of change in velocity in the time interval of 0.5 sec starting
from instant of projection is?
29.
A particle is projected with speed 10 m/s at an angle 60ᵒwith the horizontal.
Then the time after which its speed becomes half of its initial speed is?
20. A particle is projected at an
angle of 37ᵒ with the incline plane in the upward direction with the initial
velocity 10 m/s. The angle of plane is given 53ᵒ. Then the maximum height
attained by the particle from the incline plane will be?
21. A stone is projected at an angles
Ɵ with horizontal from the roof of a tall building falls on the ground after
three seconds. Two second after the projection it was again at the level of
projection. Then the height of the building is?
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