First slide

Coefficient of restitution

Question

A body from height h is dropped, if the coefficient of restitution is e, then calculate the height achieved after one bounce.

Easy

A

$h_{1} = e^{4} h$
B

$h = e h_{1}$
C

$h_{1} = e^{2} h$
D

$h = h_{1} / e$

Solution

When a body falls from height h, it strikes the ground with a velocity $u = \sqrt{2 gh}$ . Let it rebounces with a velocity v and rise to a height h₁.
$v = \sqrt{2 {gh}_{1}} \Rightarrow e = \frac{v}{u} = \sqrt{\frac{h_{1}}{h}}$
Clearly, $h_{1} = e^{2} h$

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