May 2021 1 130 Report
A spaceship fires a rocket - special relativity?

I'm doing a sample exam for my physics final on thursday, and this question confused me. There's no answer key posted, unfortunately.

'A spaceship fires a rocket with a mass of 5k at a speed 0.8c along the positive y axis in the frame of reference of the spaceship. The spaceship is moving at 0.9c along the x axis in your frame of reference.

a) What do you measure the velocity of the rocket to be?

I got 0.349c for this.

b) What do you measure the momentum of the rocket to be?

I got 1.2x10^9 kgm/s for this.

c) How much work did the spaceship do to launch the rocket?

This is the part I'm stuck on. I know the work-energy theorem says work = change in kinetic energy, and for relativity KE = (gamma - 1)mc^2, but what do I use for the v in the gamma expression? 0.349c? 0.8c? 0.9c?

It seems to me that it would probably be the speed of the rocket relative to the spaceship (0.8c), but I have no way of knowing if that's right or not.

I'd appreciate it if somebody could confirm this or correct me. :)

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