Q.Two equal masses m1 and m2 are moving along the same straight line with velocities 5 ms^-1 and -9 ms^-1 respectively. If the collision is elastic, then calculate the velocities after the collision of m1 and m2 respectively.

For a general one-dimensional elastic collision between masses $m_1$ (velocity $u_1$) and $m_2$ (velocity $u_2$, with $u_1>u_2$), simultaneously solving momentum conservation and kinetic-energy conservation gives the final velocities explicitly:

These formulas produce four instructive limiting cases, each worth memorising as a physical picture rather than a formula:

1. Equal masses ($m_1=m_2$): $v_1=u_2,\ v_2=u_1$ -- the two bodies exchange velocities completely.
2. Equal masses, target at rest ($m_1=m_2,\,u_2=0$): $v_1=0,\ v_2=u_1$ -- the incoming body stops dead and the target moves off with the incoming body's original speed.
3. A very light body hits a very heavy stationary target ($m_1\ll m_2,\,u_2=0$): $v_1\approx-u_1,\ v_2\approx0$ -- the light body simply bounces back with almost its original speed reversed (like a ball off a wall), and the heavy body is essentially undisturbed. …