Question

A rail road car of mass M is at rest on friction less rails when a man of mass 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

The man is approaching the engine with the same velocity as the car recoils backward.

Step-by-step explanation:

In this question, we can use the principle of conservation of momentum to find the velocity with which the man is approaching the engine. According to conservation of momentum, the total momentum before the man starts moving is equal to the total momentum after the man starts moving. Since the car is at rest initially, the total momentum before the man starts moving is zero. After the man starts moving, the car and the man together have a total momentum of mv, where m is the mass of the man and v is the velocity with which the car recoils backward.

Therefore, the momentum of the car after the man starts moving is -mv, since momentum is a vector quantity and the car moves in the opposite direction. So, according to conservation of momentum, -mv = 0 - mv, which implies 0 = mv - mv. Simplifying this equation gives 0 = mv - mv, which implies mv = mv. Dividing both sides of the equation by m gives v = v, which means that the man is approaching the engine with the velocity equal to the velocity with which the car recoils backward.