A ball is released in air above an incline plane inclined at an angle `alpha` to the horizontal. After falling vertically through a distance h it hits the incline and rebounds. The ball flies in air and then again makes an impact with the incline. This way the ball rebounds multiple times. Assume that collisions are elastic, i.e., the ball rebound without any loss in speed and in accordance to the law of reflection.
(a) Distance between the points on the incline where the ball makes first and second impact is `l_(1)` and distance between points where the ball makes second and third impact is `l_(2)`. Which is large `l_(1)` or `l_(2)`?
(b) Calculate the distance between the points on the incline where the ball makes second and fifth impact.

Answer

(a) `l_(2) gt l_(1) (b) `72 h sin alpha`