A ball is dropped from height H onto a horizontal floor. If the coefficient of restitution between the ball and floor is e, what is the total distance traversed by the ball before it comes to rest after infinite bounces?

Answer and explanation

Correct answer: D. H (1 + e^2) / (1 - e^2)

  1. Step 1: Distance of first drop = H.
  2. Step 2: Rebound height after 1st bounce = e^2 H; travel = 2 e^2 H (up and down).
  3. Step 3: After 2nd bounce = 2 e^4 H, and so on.
  4. Step 4: Total distance D = H + 2 e^2 H (1 + e^2 + e^4 + ...) = H + 2 e^2 H / (1 - e^2) = H [1 + e^2 / (1 - e^2) + e^2 / (1 - e^2)] = H (1 + e^2) / (1 - e^2).

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