Question

A ball falls on the ground from a height of 2.0 m and rebounds up to a height of 1.5 m. Find the coefficient of restitution. 

Answer 1

Let the velocity of the ball falling from height h₁ be u (when it approaches the ground).
Velocity on the ground,  \[u = \sqrt{2g h_1}\]

\[\Rightarrow u = \sqrt{2 \times 9 . 8 \times 2}\]

Let the velocity of ball when it separates from the ground be v.    (Assuming it goes up to height h₂)

\[\Rightarrow v = \sqrt{2g h_2}\]

\[ = \sqrt{2 \times 9 . 8 \times 1 . 5}\]

Let the coefficient of restitution be e. 
We know, v = eu 

\[\Rightarrow e = \frac{\sqrt{2 \times 9 . 8 \times 1 . 5}}{\sqrt{2 \times 9 . 8 \times 2}} = \frac{\sqrt{3}}{2}\]

Hence, the coefficient of restitution is \[\frac{\sqrt{3}}{2}\] .