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Question

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

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Solution

Given:
The mass of the railroad car is M.
The mass of the man is m.

The car recoils with a speed v, backwards on the rails.

Let the man of mass m approaches towards the engine with a velocity v' w.r.t the engine.

∴ The velocity of man w.r.t earth is v' − v, towards right.

Vcentre of mass= 0 (Initially at rest) 0 = -Mv + m(v' - v)Mv = m(v' - v)mv' = Mv + mvv' = M + mmvv' = 1 + Mmv

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