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Question
A ball with a velocity of 5 ms−1 impinges at an angle of 60˚ with the vertical on a smooth horizontal plane. If the coefficient of restitution is 0.5, find the velocity and direction after the impact.
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Solution
U1 = 5 ms-1
θ = 60°
e = 0.5
v = ?
Initial momentum = final momentum along the original line of m of the con.
∵ The coefficient of restitution is 0.5 (less than 1) the collision is inelastic
Applying component of velocities. The x component of velocity is
u sin θ = v sin Φ → (1)
But the magnitude of the y component is not the same using the coefficient of restitution
`ℓ = (v cos phi)/(u_1 cos theta) = 1` → (2)
squaring and adding (1) & (2)
`u^2 sin^2theta = v^2 sin^2phi`
`e^2 u^2 cos^2theta = v^2 cos^2 phi`
`v^2 = u^2[sin^2theta + e^2cos^2theta]`
v = u`sqrt(sin^-2theta + e^2cos^2theta)`
= 5`sqrt(sin^-2 60 + (0.5)^2 cos^2 60)`
= `5sqrt(3/4 + 0.25 xx 1/4)`
= `5sqrt(0.75 + 0.0625)`
= `5sqrt(0.8125)`
= `5 xx 0.90`
= 4.5 m/s
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