First slide

Collisions

Question

A steel ball falls from a height h on a floor for which the coefficient of restitution is e. The height attained by the ball after two rebounds is

Moderate

A

$eh$
B

$e^{2} h$
C

$e^{3} h$
D

$e^{4} h$

Solution

The velocity attained after a fall through a height h is given by
$v^{2} = 2 gh$
Thus $h \propto v^{2}$ . The velocity after first rebound is ev. Therefore, the height attained after first rebound $= e^{2} h$ . Velocity after second rebound is $e^{2} v$ . Hence the height attained after rebound is second $e^{4} h$ . Thus the correct choice is (4).

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