2D Motion of Sphere - Inclined Plane

[Keano16]

Homework Statement

A small sphere is dropped from rest at a height 'h' above a plane inclined at an angle θ to the horizontal ( < 90degrees ). Given that the sphere loses no energy on impact, show that the distance down the plane between this impact and the next is 8hSinθ.

Homework Equations

The Attempt at a Solution

Presumably, we need to consider a rotated reference frame oriented to apply to the given inclined plane. The component along the plane will have a Sinθ component, but I can't really put my finger on how to solve this.

 

[rl.bhat]

After the first impact, the ball will recoil with velocity v making an angle θ with the perpendicular to the inclined plane.
If A is the first point of impact and P is the next point of impact, then distplacement along inclined plane is
AP = vsinθ*t + 1/2*gsinθ*t^2...(1)
Along the vertical direction to the inclined plane, the displacement is zero. So
0 = vcosθ*t - 1/2*gcosθ*t^2 ...(2)
Find the value of t from the second equation and substitute in eq(1) to find AP.