A ball falls freely form a height onto and smooth inclined plane forming an angle a with the horizontal. Find the ratio of the distance between the points at which the jumping ball strikes the inclined plane. Assume the impacts to be elastic.

Explanation

The situation is shown in Fig.
Let the ball rebound from point A and return to the plane at point B, moving along the trajectory shown in diagram.
Let, AB=l
Velocity of rebound at point `A, v = sqrt(2gh)`
Velocity component perpendicular to plane = `v cos alpha`
Velocity component along the plane `= v sin alpah`
Retardation perpendicular to plane = g sin `alpha`
Acceleration along the plane = g sin `alpha`
If the ball comes to rest at this highest point after time t, then `(v cos alpha g cos alpha.t)` = 0 or `t=(v)/(g)`
Time of flight of the ball, `T = 2t =(2v)/(g)`
Range of the ball along the plane,
`l (v sin alpha) T + (1)/(2)` . g sin alpha `(4v^(2))/(g^(2))`
` = (2v^(2))/(g) sin alpha + (2v^(2))/(g) sin alpha`
`(becuae v = sqrt(2gh)) " "therefore l =8 h sin alpha`