A ball is dropped from the height `h` on an inclined plane of inclination `theta`. If the coefficient of restitution is `e`, at what distance along the plane , the ball again collides with the plane.

Explanation

Velocity along the plane remains same , `_|_^(ar)` to the plane becomes `e` times.
`_|_^(ar)` to the plane:
`0 = ev cos theta t - (1)/(2) g cos theta t^(2)`
`rArr t = ( 2ev)/(g)`
Along the plane :
`d = v sin theta t + (1)/(2) g sin theta t^(2)`
`= v sin theta ( 2ev)/(g) + (1)/(2) g sin theta ((2 ev)/(g))^(2)`
` = (2 ev^(2) sin theta)/(g) + (2 e^(2) v^(2) sin theta)/(g)`
`= ( 2ev^(2) sin theta)/(g) (1 + e)` `{v^(2) = 0 + 2gh}`
` = ( 2e xx 2gh sin theta(1 + e))/(g) = 4 e( 1 + e) h sin theta`
`= 4 e( 1 + e) h sin theta`