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Men and flatcar

N men, each with mass m$,$ stand on a railway flatcar of mass M$.$

They jump off one end of the flatcar with velocity u relative to the

car. The car rolls in the opposite direction without friction.

$($a$)$ What is the final velocity of the flatcar if all the men jump

off at the same time?

$($b$)$ What is the final velocity of the flatcar if they jump off one

at a time? $($The answer can be left in the form of a sum of terms.$)$

$($c$)$ Does case $($a$)$ or case $($b$)$ yield the larger final velocity of

the flatcar? Can you give a simple physical explanation for your

answer?