# 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 - Physics

Sum

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?

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

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 9 Centre of Mass, Linear Momentum, Collision
Q 26 | Page 161