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A glass marble is released from a height above a level floor and takes time t to hit the floor for the first time. After that, it keeps rebounding vertically. If the coefficient of restitution is e, the total time after release for which the marble keeps moving before it finally comes to rest is

1. e^t
2. e²t
3. [(1+e)/(1-e)]t
4. [(1-e)/(1+e)]t

Correct answer: [(1+e)/(1-e)]t

Solution

The first fall takes time t. Each rebound's up-down flight time forms a geometric series: T = t + 2*t*(e + e^2 + ...) = t + 2*t*e/(1-e) = t*(1+e)/(1-e).

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