Question

A ball with velocity of 5m/s impinges at angle of 60° with the vertical on a horizontal plane . If the coefficient of restitution is 0.5 find the velocity and direction after impact?

Answer 1

two components of velocity just before collision with the horizontal is given by

$v_x = 5sin60 = 4.33 m/s$

$v_y = 5cos60 = 2.5 m/s$

now after collision with the horizontal velocity of rebound will be

$v_x' = 4.33 m/s$

$v_y' = ev_y = 0.5*2.5 = 1.25 m/s$

net velocity after collision

$v_{net} = \sqrt{v_x'^2 + v_y'^2}$

$v_{net} = \sqrt{4.33^2 + 1.25^2}$

$v_{net} = 4.51 m/s$

direction after collision

$\theta = tan^{-1}\frac{v_x'}{v_y'}$

$\theta  = 73.9 degree$

so it will rebound at 73.9 degree with the vertical