Two persons each of mass $m$ are standing at the two extremes of a railroad car of mass $M$ resting on a smooth track. The person on left jumps to the left with the horizontal speed u with respect to the state of car before the jump. Thereafter, the other person jumps to the right, again with the same Two persons each of mass $m$ are standing at the two extremes of a railroad car of mass $M$ resting on a smooth track. The person on left jumps to the left with the horizontal speed u with respect to the state of car before the jump. Thereafter, the other person jumps to the right, again with the same
After left person jumps,
$0=m u+(M+m) V_{1}$
$V_{1}=\frac{-m u}{(M+m)}$
$\mathrm{u}$ is left, $V_{1}$ is right
After riaht person iumbs
$0=m u+M V_{2}$
After riqht person jumps
$V_{1}=\frac{-m u}{M}$
$\mathrm{u}$ is left, $V_{2}$ is right
(as $V_{2}>V_{1} V_{\text {Net }}$ is left)
Net velocity $=\frac{m u}{M}-\frac{m u}{M+m}$
$=\frac{m^{2} u}{M(m+M)}$ towards left