# A car and a train colliding with each other.

1. Nov 3, 2013

### GreenTea09

1. The problem statement, all variables and given/known data

A car and a train collides with each other in an elastic collision. The mass of the train is much more larger than the mass of the car. Ignore air resistance and friction from the railway tracks and roads.
Just before impact the car has a velocity of (V) train has a velocity of (-V).

What is the velocity of the car immediately after its collision with the train? Express your answer in terms of (V).
2. Relevant equations
m1u1+m2u2=m1v1+m2v2
0.5(mass of car)*v^2 + 0.5(mass of train)*V^2= 0.5*mass of car*(v1)^2 + 0.5(mass of train)*(v2)^2

3. The attempt at a solution
i tried using:
m1u1+m2u2=m1v1+m2v2
as well as conservation of K.E as the collision is elastic.
but there seem to be too many unknowns and i cant express my answer in terms of just (V)..

Last edited: Nov 3, 2013
2. Nov 3, 2013

### Nick O

Mtrain >>> Mcar. So, the initial and final momentum of the train will be approximately equal.

Do you, by any chance, remember a special approximation for an object of very small mass colliding with an object of very large mass?

Think about kicking a rubber ball directly at a brick wall. The speed of the ball will be about the same before and after hitting the wall, but in the opposite direction. This works here as well, but you need to choose a frame of reference in which the train is motionless to get the right result.