A ball is dropped from height 5 m onto a horizontal floor. The coefficient of restitution is e = 1/2. Take g = 10 m/s². If the total time until the infinite sequence of rebounds is completed is N s, find N.
Physics · Center of maas , Momentum and Collision · collision and types of collision
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Question

A ball is dropped from height 5 m onto a horizontal floor. The coefficient of restitution is e = 1/2. Take g = 10 m/s². If the total time until the infinite sequence of rebounds is completed is N s, find N.

Physics · Center of maas , Momentum and Collision · collision and types of collision

G1 Physics · Accepted Answer

Initial fall time: t0 = √(2H/g) = √(2×5/10) = 1 s. Speed just before first impact: u = √(2gH) = 10 m/s. After first rebound, upward speed is eu = 5 m/s. The complete flight time of the first rebound is T1 = 2(5)/10 = 1 s. After each collision, rebound speed is multiplied by e = 1/2, so rebound flight times form: 1, 1/2, 1/4, 1/8, ... Sum of all rebound times: T(rebounds) = 1/(1−1/2) = 2 s. Total time: T(total) = t0 + T(rebounds) = 1 + 2 = 3 s. Hence N = 3.