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Question

A ball of mass $$m$$ hits the floor with a speed $$\nu_0$$ making an angle of incidence $$\alpha$$ with the normal. The coefficient of restitution is i.e. Find the speed of the reflected ball and the angle reflection of the ball.


Solution

the component of velocity $$\nu_0$$ along common tangent direction $$\nu_0 \,sin\,\alpha$$ remain unchanged. Let $$\nu$$ be the component along common normal direction after collision. Applying relative speed of separation $$= e \times$$ (relative speed of approach) along common normal direction, we get
$$\nu = e\nu_0 \,cos \,\alpha$$
Thus, after collision components of velocity $$\nu '$$ are $$\nu_0 \,sin \,\alpha$$ and $$e\nu_0 \,cos \,\alpha$$.
$$\therefore \nu ' = \sqrt{(\nu_0 \,sin \,\alpha)^2 + (e\nu_0 \,cos \,\alpha)^2}$$
and $$tan \beta = \dfrac{\nu_0 \,sin \,\alpha}{e\nu_0 \,cos \,\alpha} = \dfrac{tan \,\alpha}{e}$$
1032782_995506_ans_afb26c96520c4cba94c930e066b50833.PNG

Physics

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