xmPuzzle 006 Bouncing on Slope

Slide9

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

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)

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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 gcosθ in the –y direction, and constant “rightward” acceleration of gsinθ in the +x direction.

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