Question:
A railroad car of mass $M$ is at rest on frictionlessrails when a man of mass $m$ starts moving on the car towards the engine. If the car recoils with a speed $v$ backward on the rails, with what velocity is the man approaching the engine?
Solution:
C.OL.M
$V_{1}=$ velocity with which man in car approaches.
$\Rightarrow(M+m) V=m V_{1}$
$\Rightarrow V_{1}=\frac{(M+m) V}{m}=\left(1+\frac{M}{m}\right) V$