Question

A very bouncy ball is dropped from a height of 2.47 m to an asphalt playground surface and the height of its 4 th bounce is measured to be 1.71 m. Find the coefficient of restitution of the ball for a collision with asphalt.

Answer 1

0.912

Step-by-step explanation:

Given that

Height of bouncing of the ball, h = 1.71 m

Number of times the ball bounced, n = 4 times

Height from which the ball was dropped, H = 2.47

First, let's start by defining what coefficient of restitution means

Coefficient of Restitution, CoR is the "ratio of the final to initial relative velocity between two objects after they collide. It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision."

It is mathematically represented as

CoR = (velocity after collision) / (velocity before collision)

1.71 = 2.47 * c^4, where c = CoR

1.71/2.47 = c^4

c^4 = 0.6923

c = 4th root of 0.6923

c = 0.912