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.

中文翻译：

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在斜坡上弹跳

我们分析了倾斜表面上方上山发射的点状质量弹丸的运动，该弹丸从该表面反弹而没有损失能量。我们证明了连续的反弹在相等的时间间隔内发生，并获得了运动反向和弹头下降之前的上坡反弹次数的明确公式。此外，我们显示了每次弹跳时，弹丸会升至表面上方相同的高度，并且我们确定了必要条件和充分条件，在这种条件下，弹丸会在反转时恢复其路径。