A ball is tossed and lands PERPENDICULARLY on a slope. Describe the subsequent trajectory of the ball. (Assume elastic collisions and negligible air resistance)

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Answer:

The ball will always bounce back to the same “height” above the slope, and the distance between bounces follow the arithmetic progression of 1, 3, 5, 7… units. (See below)

The easiest to see this is to resolve everything into two perpendicular components *x* and *y*: *x* parallel to the slope, and *y* perpendicular to the slope. It is then clear that the ball has a constant “downward” acceleration of *g*cos*θ* in the –y direction, and constant “rightward” acceleration of *g*sin*θ* in the +x direction.

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