A small ball falling vertically downward with constant velocity 4m/s strikes elastically a massive i

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A small ball falling vertically downward with constant velocity 4m/s strikes elastically a massive inclined cart moving with velocity 4m/s horizontally as shown. The velocity of the rebound of the ball is

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Sol. $e = \frac{v_{sep}}{v_{app.}}$vapp = 4 cos 45° + 4 cos 45°= $\frac{8}{\sqrt{2}}$vsep = v1 – 4 cos 45°e = 1 = $\frac{v_{1} - \frac{4}{\sqrt{2}}}{\frac{8}{\sqrt{2}}}$ ⇒ $v_{1} = \frac{12}{\sqrt{2}}$v1 = velocity of ball ⊥ar to the surface.v2 = velocity of ball along the surface.= 4 sin 45° = $\frac{4}{\sqrt{2}}{m/}s$Speed = $\sqrt{v_{1}^{2} + v_{2}^{2}}$= $\sqrt{\left( \frac{12}{\sqrt{2}} \right)^{2} + \left( \frac{4}{\sqrt{2}} \right)^{2}}$= $\sqrt{\frac{160}{2}}$ = $\sqrt{80}$

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