# Homework Help: Quick Relativity problem set up

1. Jun 2, 2014

### MostlyHarmless

1. The problem statement, all variables and given/known data
(Verbatim) A particle moves with speed .9c along the x'' axis of frame S'', which moves with speed .9c in the positive x'-direction relative to frame S'. Frame S' moves with speed .9c, in the positive x-direction, relative to S. a.) Find the speed of the particle relative to S', and b.) S''.

2. Relevant equations
Relativistic Velocity Transform: $$u'_x= \frac{u_x-v}{1-\frac{vu_x}{c^2}}$$

3. The attempt at a solution
My question is more or less just about the interpretation of the question.

The first line, does that mean, the particle's rest frame is S''? Or that the particle is at rest in S'' which is moving at .9c?

2. Jun 2, 2014

### tms

It means that the particle is moving in S, S' is moving with respect to S, and S'' is moving with respect to S'. Otherwise there is no point in asking for the speed in S''.

3. Jun 3, 2014

### vanhees71

No, the question tells you that the particle is moving with 0.9c in reference frame S" and S" is moving with respect to S' with a velocity of 0.9c which in turn moves with speed 0.9c wrt. S. It's not said that any of these systems is the restframe of the particle. Just calculate!

Hint: It's easier to work with covariant quantities. Since all boosts are in the same direction, it's useful to work with rapidities!

4. Jun 3, 2014

### tms

If the particle is moving at the given speed wrt S'', why does the question ask for the particle's speed wrt S''?

5. Jun 3, 2014

### dauto

That's a typo. They want you calculate the speeds relative to S' and S - not S' and S''. The speed relative to S'' is given.