A girl throws a ball with initial velocity $v$ at an inclination of $45 °$ . The ball strikes a smooth vertical wall at a horizontal distance d from the girl and after rebouncing returns to her hand. The coefficient of restitution between the wall and the ball is $\frac{k g d}{v^{2} - g d}$ where ‘k’ is ____

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Detailed Solution

$T = \frac{d}{(v / \sqrt{2})} + \frac{d}{(e v / \sqrt{2})} = (1 + \frac{1}{e}) \frac{\sqrt{2} d}{v}$

$where T = \frac{2 Vsin 45^{\circ}}{g}$

$\frac{2 v / \sqrt{2}}{g} = (1 + \frac{1}{e}) \frac{\sqrt{2} d}{v} \Rightarrow e = \frac{gd}{v^{2} - gd}$

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