A ball strikes a smooth fixed vertical wall with speed 10 m/s. Its velocity makes an angle 60° with the normal to the wall. The coefficient of restitution is e = 3/5. If its speed just after collision is 2√N m/s, find N.
Physics · Center of maas , Momentum and Collision · collision and types of collision
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Question

A ball strikes a smooth fixed vertical wall with speed 10 m/s. Its velocity makes an angle 60° with the normal to the wall. The coefficient of restitution is e = 3/5. If its speed just after collision is 2√N m/s, find N.

Physics · Center of maas , Momentum and Collision · collision and types of collision

G1 Physics · Accepted Answer

Resolve the incident velocity into components normal and tangential to the wall. Normal component: u_n = 10cos60° = 5 m/s. Tangential component: u_t = 10sin60° = 5√3 m/s. For a smooth wall, tangential velocity is unchanged. For restitution e = 3/5, the normal component reverses direction and its magnitude becomes v_n = eu_n = (3/5)(5) = 3 m/s. Therefore final speed: v = √(v_n² + v_t²) = √[3² + (5√3)²] = √(9 + 75) = √84 = 2√21 m/s. Hence N = 21.