A particle moves up and down a frictionless plane between bounces from a perfect

Question

A particle moves up and down a frictionless plane between bounces from a perfectly elastic wall at the bottom, as shown a) Assume the angle is suddenly changed (meaning the particle does not have time to move relative to the plane) when the particle has just bounced off the bottom wall, the angle going from theta(as shown) to 2 theta. b) Now assume the angle is very gradually changed from theta to 2 theta, meaning many bounces take place during the change. What is the maximum height above ground of the bounces after the change?

Explanation / Answer

As the ball experiencing perfectly elastic collision, so the change in total energy must be zero. The initial kinetic energy must be equal to the final potential energy. So with the change in the angle doesnt change the height reached by the ball.

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