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A ball is dropped from height H onto a horizontal floor. If the coefficient of restitution is e, find the total time elapsed before the ball finally comes to rest.

1. sqrt(2H/g) * ((1 - e)/(1 + e))
2. sqrt(2H/g) * ((1 + e)/(1 - e))
3. sqrt(2H/g) * ((1 + e²)/(1 - e²))
4. sqrt(2H/g) * ((1 - e²)/(1 + e²))

Correct answer: sqrt(2H/g) * ((1 + e)/(1 - e))

Solution

First fall takes t0 = sqrt(2H/g). Each subsequent bounce contributes 2*eⁿ*t0; summing the geometric series gives total time = t0*(1+e)/(1-e).

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