A ball with a mass of 2 kg is rolling at 25 m/s and elastically collides with a resting ball with a mass of 2 kg. What are the post-collision velocities of the balls?

1 Answer
Nov 11, 2017

The velocities of the balls are =0ms^-1 and =25ms^-1

Explanation:

As the collision is elastic, there is conservation of linear momentum and conservation of kinetic energy

Let the velocity before collision be u_1ms^-1 and u_2ms^-1

Let the velocity after collision be v_1ms^-1 and v_2ms^-1

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

Here, we have

m_1=m_2=2kg

u_1=25ms^-1

u_2=0ms^-1

Therefore,

v_1+v_2=25

v_1^2+v_2^2=25^2=625

v_1=25-v_2

(25-v_2)^2+v_2^2=625

625-50v_2+v^2+v^2=625

2v_2^2-50v_2=0

2v_2(v_2-25)=0

v_2=25 and v_1=0