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A ball in projected from a given point with velocity $u$ at some angle with the horizontal and after hitting a vertical wall returns to the same point. If the maximum distance of the point from the wall is d and e is the coefficient of restitution , then

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$d = \frac{u^{2}}{(1 + e) g}$

$d = \frac{(1 + e) u^{2}}{e g}$

$d = \frac{(1 - e) u^{2}}{(1 + e) g}$

$d = \frac{e u^{2}}{(1 + e) g}$

answer is D.

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Detailed Solution

$\frac{x}{u \cos α} + \frac{x}{eucos α} = T = \frac{2 u \sin α}{g} o r x = \frac{e u^{2} \sin 2 α}{(1 + e) g} \Rightarrow x_{\max} = d = \frac{e u^{2}}{(1 + e) g}$

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