- #1

Ravenatic20

- 30

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## 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?