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

Answer:

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

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

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