From a point on a smooth floor of a room a ball is shot to hit a wall. The ball then returns back to the point of projection. If the time taken by the ball in returining is twice the time taken to reach the wall, find twice the time taken to reach the wall, find the coefficient of restitution between was and ball.

Answer

`(1)/(2)`

Explanation

Since velocity along horizontal does not change is case of projectile motion

`therefore u cos theta = v cos alpha` …….(i)
For collisoin with wall
`v' cos beta = e(v cos alpha) = e u cos theta` ....(ii)
Let `t =` time taken by the ball of collide with wall.
then `t(u cos theta) = d` ....(iii)
`2t =` time taken by ball to come back to point `P`.
then `(2t)(u cos theta) = d` ....(iv)
[using (ii)]
from (iii) & (iv) `e = (1)/(2)`.