If after impact the ball having mass 30kg reverse its direction of motion and moves with velocity 6m/s, then determine the coefficient of restitution between the two balls.

$m_1=20 kg\hspace{1.8cm} m_2=30 kg \\ u_1=10 m/s \hspace{1.8cm} u_2= -5 m/s \\ V_1= ? \hspace{1.8cm} V_2=6 m/s \\ e= ? $

By Law of conservation of momentum,

$m_1 u_1+ m_2 u_2=m_1 V_1+ m_2 V_2 \\ 20 ×10+30×(-5)= 20×V_1+30×6 \\V_1= -6.5 m/s $

Coefficient of restriction,

$e= \dfrac {V_2-V_1}{u_1-u_2 } = \dfrac {6+6.5}{10+5} \\ e=0.8333 $