# Special Relativity Velocity Transformation

1. Oct 14, 2009

### mike_romeo

Hi,
I'm struggling with a special relativity question

Two particles are travelling in an inertial frame in perpendicular directions to each other at velocity v. Calculate the velocity of each particle relative to the other

I'm not sure how to approach it. In the past any velocity transformations I have done have always been for particles travelling in the same or opposite directions, not orthogonally?

Any help appreciated!

2. Oct 14, 2009

### Gear300

If one of the particles (particle I) was intelligent and was able to 'see' the other one, it would see that the other particle was coming in at an angle, which is due to particle I moving toward the other particle and also due to how the other particle is moving in the given direction.

3. Oct 14, 2009

### gabbagabbahey

Hi mike romeo, welcome to PF!

Try treating the problem using 3 frames of reference; the lab frame $S$, particle 1's rest frame $S'$ and particle 2's rest frame $S''$....set up your coordinate axes however you want and then calculate away...

4. Oct 18, 2009

### mike_romeo

Thanks for the replies, sorry for taking a while to get back to you both.

I got it in the end after countless pages of working out trying different methods and the ones you mentioned.

Thanks again