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A ball is dropped onto a fixed inclined plane and bounces elastically (coefficient of restitution = 1). After successive bounces, the ranges measured along the incline between consecutive bounce points are R1, R2, and R3. If R2 = (R1 + R3) / a, find the value of a.

1. 5.5
2. 6
3. 6.5
4. 2

Correct answer: 2

Solution

For elastic bouncing on an inclined plane, the ranges form an arithmetic progression (R1: R2: R3 = 1: 2: 3), so R2 = (R1 + R3)/2, giving a = 2.

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