Question

Two billiard balls, assumed to have identical mass, collide in a perfectly elastic collision. Ball A is heading East at 12 m/s. Ball B is moving West at 8.0 m/s. Determine the post-collision velocities of Ball A and Ball B.

Answer 1

Ball A will move towards West with speed 8 m/s

Ball B will move towards East with speed 12 m/s

Step-by-step explanation:

As we know that during collision there is no external force on the system

So here we can use momentum conservation for finding the final velocities of two balls

so we have

`m_1v_(1i) + m_2v_(2i) = m_1v_(1f) + m_2v_(2f)`

since two balls are identical so we have

`m_1 = m_2`

`m(12) - m(8) = mv_1 + mv_2`

`v_1 + v_2 = 4`

also we know that for elastic collision we have

`v_(2f) - v_(1f) = v_(1i) - v_(2i)`

so we have

`v_2 - v_1 = 12 - (-8)`

`v_2 - v_1 = 20`

so we have

`v_2 = 12 m/s` Towards East

`v_1 = 8 m/s` Towards West