Show momentum is conserved in two different frames (relativity)

[Ravenatic20]

Homework Statement

A 2000-kg car moving with a speed of 20 m/s collides with and sticks to a 1500-kg car at rest. Show that because momentum is conserved in the rest frame, momentum is also conserved in a reference frame moving with a speed of 10 m/s in the direction of the moving car.

Homework Equations

Not sure

The Attempt at a Solution

Let's have the larger (2000-kg) car be mass M, and the smaller (1500-kg) car to be mass m. Car M is traveling at speed v. After the collision, the two cars become one mass (M+m) and its velocity we will call v'.

To an observer on the ground...
mv + 0 = (M+m) v'
v' = MV/(M+m)

To an observer in a moving frame...
M is moving at speed V-v (towards the smaller car, m) and m is moving at speed -v (towards the larger vehicle, M). After the collision, (M+m) is moving at speed v'-v.
M(V-v) - mv = (M+m)(v'-v)
MV - Mv - mv + Mv + mv = (M+m)v'
v' = MV/(M+m)

These two equations are the same, meaning the final speed of the indecent is v' from any observer. Does this mean momentum is also conserved in a reference frame? If I'm on the right track, what good would it do plugging in numbers?

 

[Brian_C]

Re-read the question. You need to prove that conservation of momentum in the rest frame implies conservation of momentum in the moving frame. You're also not being consistent with your notation. The v in your first set of equations represents the speed of the bigger car, but in the second set of equations it represents the relative speed of the moving frame.

 

[Ravenatic20]

You're right. I ended up solving the problem. Thanks anyways.

Consider this problem solved.