Bouncing on a slope

摘要

We analyze the motion of a point-mass projectile shot uphill above a slanted surface, which bounces from it without loss of energy. We show that consecutive bounces occur in equal time intervals and obtain an explicit formula for the number of uphill bounces before the motion reverses and the projectile heads downhill. Additionally, we show that the projectile rises to the same height above the surface on each bounce, and we determine the necessary and sufficient conditions under which it will retrace its path upon reversal.