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?  

Answer 1

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.
\[V_{centre of mass} = 0 (\text{Initially at rest })\]
\[ \therefore 0 = - Mv + m(v' - v)\]
\[ \Rightarrow Mv = m(v' - v)\]
\[ \Rightarrow mv' = Mv + mv\]
\[ \Rightarrow v' = \left( \frac{M + m}{m} \right)v\]
\[ \Rightarrow v' = \left( 1 + \frac{M}{m} \right)v\]