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A ball of mass m hits the floor with a s...

A ball of mass `m` hits the 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 and the angle of reflection of the ball.

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The component of velocity `v_(0)` along common tangent direction `v_(0)sinalpha` will remain unchanged. Let `v` be the component along common normal direction after collision. Applying relative sped of separation `=exx` ( relative speed of approach) along common normal direction we get
`v=ev_(0)cosalpha`
Thus, after collision components of velocity `v'` and `v_(0)sinalpha` and `ev_(0)cosalpha`.

`:. v'=sqrt((v_(0)sinalpha)^(2)+(ev_(0)cosalpha)^(2))`
and `tanbeta=(v_(0)sinalpha)/(ev_(0)cosalpha)=(tanalpha)/e`
`:. v'=v_(0)` and `beta =alpha`
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