Special Relativity Rocket Problem

[dpeagler]

1. Two rockets, A and B, leave a space station with velocity vectors v_a and v_b relative to the station frame S, perpendicular to each other.

(a) Determine the velocity of A and to B, v_ba.

(b) Determine the velocity of B relative to A, v_ab.

(c) Explain why v_ab and v_ba do not point in opposite directions

Homework Equations

U' = ( U - v ) / (1 - (vU/c^2) )

The Attempt at a Solution

I have mulled over this problem for a while now and I know that since we don't have values for the velocities that U' will be some percent of U, but I am getting confused on the fact that the two velocity vectors are perpendicular to each other, which I didn't think would matter.

Perhaps there is something to the vector being extended by both vectors simultaneously increasing?

Any help is greatly appreciated.

 

[dpeagler]

I completed part A and B, but have no idea why the two vectors aren't opposite of each other. If anyone could just nudge me into the correct thinking that would be amazing.

 

[hikaru1221]

I'm totally not amazing, but I may share my opinion on this. The conventional idea about space is that space does NOT change howsoever you look at it, regardless of the reference frame you choose. That the distance between 2 points is fixed regardless of reference frame is one example. That means, space is an absolute thing. But, as far as I understand, relativity theory has pointed out that notion is not true, i.e. space is dependent on the viewpoint. Therefore I think comparing the direction of Vab and Vba is quite pointless (not really "pointless" because at least, it bugs us to think more about relativity ). Each vector is defined in its corresponding reference frame, in its own space. There is no reason to be surprised at that Vab and Vba "are not in opposite direction", as that's meaningless when it comes to relativity.
But, what do I know?