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)
$$\begin{gathered} \Rightarrow v=\sqrt{2g{h}_2} \\ =\sqrt{2\times 9.8\times 1.5} \end{gathered}$$

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 $\frac{\sqrt{3}}{2}$.