When a very light object such as a ping$-$pong ball hits head$-$on a very heavy object that is at rest, such as a bowling ball, and the collision is elastic, the light object bounces back with a speed that is only very slightly less than the initial speed. It's like bouncing off a wall. The heavy object recoils with a speed that is very small compared to the speed of the light object.

By solving exactly the equations for momentum and energy conservation $($and assuming an elastic collsion$),$ it can be shown that the following results are true, without making approximations, and these exact results can be used to explore how good the approximate results are. The light object has a mass $m,$ initial speed $v_i,$ and final speed $v_f.$ The heavy object has a mass $M$ and a final speed $V.$

$v_f=\frac{M-m}{M+m}{v}_i,$ so $v_f$~~$v_i$ if $M>>m.$

$V=\frac{2m}{M+m}{v}_i,$ so $V$ is nearlyzero if $M>>m.$

Suppose $m=1kg$ and its initial speed $v_i=60\frac{m}{s}.$ Suppose $M=100kg$ and this heavy object is initially at rest$).$