A body is fired from point P and strikes at Q inside a smooth circular wall as shown in the figure. It rebounds to point S (diametrically opposite to P). The coefficient of restitution will be

Engineering

Physics

Collision

Question

tan α

tan² α

cot α

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Let v₁ and v₂ be the speed of the body before and after striking.
v₁ sin α = v₂ cos α (as there is no friction)

${ev}_{1} cosα = v_{2} \cos (\frac{π}{2} - α)$

$\Rightarrow e = \frac{v_{2} sinα}{v_{1} cosα} = \tan^{2} α$ .