A rho meson of rest mass 768 MeV/c^2 and total energy of 960 MeV decays into 2 pions, neutral and positive with rest masses 135 and 139.6 MeV/c^2 respectively. Show that the neutral pion has a speed of 0.93588c with respect to the centre of mass frame and that it's momentum, energy and lorentz factor are 735.6 MeV/c, 747.9 MeV and 5.54 respectively.

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I really hate special relativity. People think it's cool but it's so illogical and doesn't benefit us in any way.

Anyway here's my feeble attempt:

the rho meson is moving relatvistically, so it's total energy is a summation of it's rest mass and kinetic energy, this can be condensed into:

E = yM. I found y as 1.25 and therefore b = 0.6. rho moves at 0.6c in the laboratory frame.

Energy and momentum must be conserved. So total energy before = total energy after. Total momentum before = total momentum after.

E^2 = p^2 + m^2

so p = 576 MeV/c

So now I have momentum and energy at the beginning and they must be the same at the end.

The problem is, the pions are both going to be moving at high speeds.. How do I go about finding their speeds, momentums and energies?

My question got deleted..

I just found the energies of the 2 particles as 384.8 and 575.2 MeV. This seems kind of wrong seeing as the 2 particles have almost the same mass...

I really need help, I don't mean to sound impatient but I really want to do well in this homework, my last relativity homework was not that great...

Is there no Physics expert to help? My life over!

Pfft, don't even bother replying. I solved it myself.