A ball is thrown vertically downward with speed m/s to hit a horizontal surface as shown in the figure. The coefficient of restitution for the collision is and friction coefficient . Calculate the speed (m/s) of the ball just after the collision.

Engineering

Physics

Collision

Instantaneous Centre and Instantaneous Axis of Rotation

Question

A ball is thrown vertically downward with speed $5 \sqrt{2}$ m/s to hit a horizontal surface as shown in the figure. The coefficient of restitution for the collision $\frac{1}{2}$ is and friction coefficient $\frac{1}{3}$ . Calculate the speed (m/s) of the ball just after the collision.

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$NΔt = \frac{3 mv}{2}$

$μNΔt = {mv}_{x}$

$\Rightarrow v_{x} = \frac{3 μv}{2}$

$∴ speed = \frac{v}{2} \sqrt{1 + 3 μ^{2}} = 5 m / s$