How to Find Particle Speed in Different Reference Frames Using Relativity?

[MostlyHarmless]

Homework Statement

(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''.

Homework Equations

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

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?

 

[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''.

 

[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!

 

[tms]

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.

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

 

[dauto]

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

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.