Question

A rail road car of mass M is at rest on friction less rails when a man of mass 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?

Answer 1

Suppose the man approaches the ensive in the velocity $V_0$ & car goes back in the velocity then the speed of man e.r.t earth will be $V_0-V$

Center of mass should not move as No internal force

so $m_1{v}_2+m_2{v}_2=0$

$-Mv+m(v_0-V)=0$

$-$ve because move in opposite direction to that of the man

$\Rightarrow -mv+m{v}_0-mV=0$

$\Rightarrow v_0=\frac{v(m+M)}{m}$