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A small ball strikes obliquely a smooth horizontal surface. The components of its velocity just before impact are: horizontal component (along surface) = 4 m/s, vertical component (downward, perpendicular to surface) = 2 m/s. The coefficient of restitution between ball and surface is 1/2. Find the horizontal component vₓ and vertical component v_y of velocity just after impact.
- vₓ = 4 m/s, v_y = 1 m/s
- vₓ = 2 m/s, v_y = 1 m/s
- vₓ = 2 m/s, v_y = 2 m/s
- vₓ = 4 m/s, v_y = 2 m/s
Correct answer: vₓ = 4 m/s, v_y = 1 m/s
Solution
A smooth surface means no friction, so the component of velocity parallel to the surface (x-direction) is unaffected. The perpendicular component (y-direction) is reversed and reduced by the coefficient of restitution e = 1/2.
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