Resultant Velocities in 2D (Relativistic)

[jeffbarrington]

Homework Statement

Here's the question:

http://i.imgur.com/zs130b3.png

Homework Equations

Just the usual Lorentz transform matrix etc.

The Attempt at a Solution

http://imgur.com/4Oipfu9
Now, the last line is clearly incorrect, since it tends towards infinite relative speed as v --> c. Of course the initial answer of sqrt(2)v for the first part is fine because that isn't relative speed (I am pretty sure I have this part right - let me know if not). I have a feeling I can't 'Pythagorise' the 3-velocity part of Vrel4 to get a magnitude, but this is a bit of a guess. Vrel4 still seems to obey the V.V = (+/-)c^2 inner product identity so that points towards it being the correct 4-vector, although I may be wrong about that.

Thanks for any help.

(check the imgur links, pictures didn't work)

 

[Ray Vickson]

Homework Statement

Here's the question:

http://i.imgur.com/zs130b3.png

Homework Equations

Just the usual Lorentz transform matrix etc.

The Attempt at a Solution

http://imgur.com/4Oipfu9
Now, the last line is clearly incorrect, since it tends towards infinite relative speed as v --> c. Of course the initial answer of sqrt(2)v for the first part is fine because that isn't relative speed (I am pretty sure I have this part right - let me know if not). I have a feeling I can't 'Pythagorise' the 3-velocity part of Vrel4 to get a magnitude, but this is a bit of a guess. Vrel4 still seems to obey the V.V = (+/-)c^2 inner product identity so that points towards it being the correct 4-vector, although I may be wrong about that.

Thanks for any help.

(check the imgur links, pictures didn't work)

I don't know what you did, since you posted all your work in an image and I do not look at those---only at typed solutions. (Most other helpers won't look at it either.) Consult the PF Guidelines.

However, the way I would approach the problem if I were solving it would be to go into the rest-frame of ejected particle 1, and use Lorentz-transformation equations go get the (vector) velocity of ejected particle 2 in that new frame. From that, the relative speed is easy to get.