A ball of a mass m hits the floor with as speed v making an angle of incidence `theta` with the normal. The coefficient of restitution is e. Find the speed of the reflected ball and the angle of reflection of the ball.
`

Explanation

Suppose `upsilon^(')` is speed after collision and `theta^(')` is angle of reflection, Figure.
During collision, the floor exerts a force on the ball along the normal. There is no force parallel to the surface. Therefore, velocity component fo ball parallel to the floor remains constant, i.e.,
`upsilon^(')sin theta^(')=upsilonsintheta` ...(i)
From component normal to the floor,
velocity of separation `=upsilon^(')cos theta^(')`
velocity of approach `=upsilon cos theta`
`:. (upsilon^(')cos theta)/(upsiloncos theta)=e`
`upsilon^(')cos theta^(')=eupsiloncos theta` ..(ii)
From (i) and (ii)
`upsilon^(')=upsilonsqrt(sin^(2)theta+e^(2)cos^(2)theta)` and `tan theta^(')=(tantheta)/(e)`
`:. theta^(')=tan^(-1)((tantheta)/(e))`