A ball is dropped from height H on to a horizontal surface. If the coefficient of restitution is e then the total time after which it comes to rest is

Question

Aicharya · Accepted Answer

The time it takes for the ball to fall from a height is given by

$t = \sqrt{\frac{2 H}{g}}$

The height up to which the ball bounces after the $n^{th}$ collision from the floor is

$H_{n} = e^{2 n} H$

$t = \sqrt{\frac{2 H}{g}} + 2 \sqrt{\frac{2 H_{1}}{g}} + 2 \sqrt{\frac{2 H_{2}}{g}} + \dots \infty$
$t = \sqrt{\frac{2 H}{g}} (1 + 2 e + 2 e^{2} + \dots \dots . . \infty)$
$t =$ $\sqrt{\frac{2 H}{g}} (\frac{1 + e}{1 - e})$

A ball is dropped from height H on to a horizontal surface. If the coefficient of restitution is e then the…

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