Question

Two men, each of mass m, stand on the edge of a stationary car and jump off with a horizontal velocity u relative to the car, first simultaneously and then one after the other. If friction be negligible, in which case will they impart greater speed to the car?

Answer 1

First case:
initial system rest
$0=mu+mv-mv$
$v=0$
second case:
when left person jumps off the case
$0=-mu+(M+m)v$
$v=\frac{mv}{M+m}$
when right person jumps off
$0=mu-m{v}^{\prime }$
$v^{\prime }=\frac{mu}{M}$