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Special Relativity: Relative speeds of particles

  1. Oct 9, 2007 #1

    OK, we have started all this special relativity stuff, and I must admit I am confused, all this Inertial Reference Frame stuff :S

    Here's the problem:
    Two particles are fired at the same time from a point, with equal speed u, in orthogonal directions.

    Show that the relative speed of one particle with respect to the other is:

    u[tex]_{R}[/tex] = u(2 - [tex]\frac{u^{2}}{c^{2}}[/tex])[tex]^{\frac{1}{2}}[/tex]

    2. Relevant equations

    Lorentz Transformation Equations
    The given solution

    3. The attempt at a solution

    OK, well what I have gathered is that I must pick for the observer a frame where one of the particles is at rest, right? And then I tried to transform the velocity of the other particle with respect to this one.
    So I tried, using normal non-relativistic ideas, to obtain via Pythagoras the relative speed, which was [tex]\sqrt{2u^{2}}[/tex]. Then I tried to operate using gamma on this velocity. However, it did not seem to get me anywhere :S
    I'm bad at explaining this :S but I thought that maybe my problem was that I chose a frame which is at rest, but one particle is still moving inside the frame (?) if that makes any sense. The fact that the particles are in two dimensions is the confusion, I could calculate the relative velocity if they were in one axis just fine, my problem is this second direction.

    Any guidance? I don't want the answer, that won't help me understand this tricky subject, just a little hint on all this I.R.F. stuff and what I've done wrong.

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 9, 2007 #2


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    Staff Emeritus
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    Gold Member

    Have you derived the rules for addition or subtraction of velocities? If you have, you need to make sure you understand them. If not, you are probably expected to simply plug into the formula for relative velocity calculation. No doubt, the formula itself will be found in your text.
  4. Oct 9, 2007 #3
    Hmm, we didn't go over velocity sums in class, and i don't see any formula for it :S

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