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)