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.

A ball is dropped from the height h on an inclined plane of inclinatio

1.	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.
Answer» Solution :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`