A ball with a mass of 2 kg is rolling at 6 m/s and elastically collides with a resting ball with a mass of 9 kg. What are the post-collision velocities of the balls?

1 Answer
Sep 1, 2017

The velocity of the first ball is =-3.82ms^-1
The velocity of the second ball is =2.18ms^-1

Explanation:

As the collision is elastic, we have conservation of linear momentum and conservation of kinetic energy.

m_1u_1+m_2u_2=m_1v_1+m_2v_2

1/2m_1u_1^2+1/2m_2u_2^2=1/2m_1v_1^2+1/2m_2v_2^2

so,

2*6+9*0=2v_1+9v_2,

=>, v_1=(12-9v_2)/(2)........................(1)

1/2* 2*6^2+1/2*9*0=1/2*2*v_1^2+1/2*9*v_2^2

2v_1^2+9v_2^2=72..........................(2)

Solving for v_1 and v_2 from equations (1) and (2)

2*((12-9v_2)/(2))^2+9v_2^2=72

(12-9v_2)^2+18v_2^2=144

144-216v_2+81v_2^2+18v_2^2=144

v_2(99v_2-216)=0

v_2=0 or v_2=216/99=2.18ms^-1

v_1=1/2(12-9*2.18)=-3.82ms^-1