How High Will the Ball Bounce on an Inclined Plane?

[Faefnir]

A ball, which can be regarded as pointin all its effects, falls steady , subject only to the weight force, on an inclined plane of an angle α with respect to the horizontal from a height h computed from the impact point. The ball bounces elastically. Get the d height can reach the ball and the falling parabola characteristics after the impactAfter impact vertical speed:

$$ v_{y} = \sqrt{2gh} \cos (2 \alpha) $$Why $\cos (2 \alpha)$? There is a mathematical explanation for this? Yes, I know about vectorial speed components, but why exactly this corner?

 

[Doc Al]

What's the relationship between the angle of incidence and the angle of reflection when something bounces elastically off of a surface?

 

[Faefnir]

angle of incidence = the angle of reflection

 

[Doc Al]

angle of incidence = the angle of reflection

Right! So draw yourself a diagram of the initial and final (pre and post collision) velocity vectors, showing the angle between them. Then find the vertical component of that final velocity.