A staircase has each step of height h and width x. A ball strikes the centre point of a step with velocity `v` making an angle `theta` with the vertical. It rebounds and strikes the centre point of the next step. Once again it rebounds and hits the centre point of the next step and so on.

Assume that there is no friction between the ball and the steps and coefficient of restitution is e.
(a) Show that each time after hitting a step, the ball climbs to the same height (i.e., heights like AB and CD shown in figure are equal).
(b) Find h and x.

Answer

(b) `h=(v^(2)cos^(2)theta(1-e^(2)))/(2g)`
`x=(e+1)(v^(2))/(2g)sin theta`