A small ball of mass m collides with a rough wall having co-efficient of friction $μ$ at an angle $θ$ with the normal to the wall. If after collision the ball moves with angle $α$ with the normal to the wall and the coefficient of restitution is ‘e’, then the reflected velocity $v$ of the ball just after the collision is $v = \frac{u}{\sin α} [\sin θ - μ \cos θ (e + x)]$ where ‘ $x$ ’ is ____

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Detailed Solution

$mVcos α - (- mucos θ) = \int Ndt$

$mVsin α - musin θ = - \int μ Ndt$

and $e = \frac{Vcos α}{ucos θ} \Rightarrow Vcos α = eucos θ$

$mVsin α - musin θ = - μ (mVcos α + mucos θ)$

$∴ V = \frac{u}{\sin α} [\sin θ - μ \cos θ (e + 1)]$

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