A railroad car of mass M is at rest on frictionless rails when a man of mass in 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?

Mass of man = m

Mass of the car = M


Initial velocity of man = u1


Initial velocity of the car, u2 = 0


Velocity of man in the car = Recoil velocity of the car = v


Applying conservation of momentum,


mu1 + Mu2 = (m+M)v


mu1 + 0 = (m+M)v


u1 = (m+M)v/m


u1 = v(1+M/m)


⇒ Velocity with which man approaches the engine = v(1+M/m)


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