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Question

A ball of mass m hits a floor with a speed $$v_0$$ making an angle of incidence $$\alpha$$ with the normal. The coefficient of restitution is e. Find the speed of the reflected ball.


A
(v0sinα)2+(ev0cosα)2
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B
(v0sinα)2(ev0cosα)2
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C
(v0cosα)2+(ev0sinα)2
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D
(v0sinα)+(ev0sinα)
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Solution

The correct option is A $$\sqrt {(v_0\, sin\, \alpha)^2\, +\, (ev_0\, cos\, \alpha)^2}$$
Answer is A.
The component of velocity $$v_0$$ along common tangential direction $$v_0$$ sin $$\alpha$$ will remain unchanged. Let v be the component along common normal direction after collision. Applying, Relative speed of separation = e (Relative speed of approach) along common normal direction, we get
Thus, after collision components of velocity v' are $$v_0$$ sin $$\alpha$$ and $$ev_0$$ cos $$\alpha$$
Therefore, $$v'\, =\, \sqrt {(v_0\, sin\, \alpha)^2\, +\, (ev_0\, cos\, \alpha)^2}$$
Hence, the speed of the reflected ball is $$v'\, =\, \sqrt {(v_0\, sin\, \alpha)^2\, +\, (ev_0\, cos\, \alpha)^2}$$

315158_300583_ans.jpg

Physics

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