I hope someone can help me out with this one.... I attempted tosolve it but get

Question

I hope someone can help me out with this one.... I attempted tosolve it but get stuck equating the energies for the 2 photons...it goes:
"A neutral pion traveling along the x axis decays into 2photons, one being ejected exactly forward, the otherexactly backward. The first photon has exactly 3times the energy of the second. Prove that the originalpion had a speed 0.5c "
any help would be appreciated... thanks
"A neutral pion traveling along the x axis decays into 2photons, one being ejected exactly forward, the otherexactly backward. The first photon has exactly 3times the energy of the second. Prove that the originalpion had a speed 0.5c "

Explanation / Answer

Let P be the energymomentum of the photon by momentum conservation alongx-axis      P= P1 -P2          P =(3E2 - E2) / c     P = 2E2 / c........eq(1) P1 , P2 arethe momentums of the photon ejected in the same    direction and oppsite directions respectively .    and by energyconservation    3E2 +1E2 = mc^2      4E2 = mc^2.................eq(2)        m= mo / [1-(v^2/c^2)]        m= mo / [1-(v^2/c^2)]    from above twoequaions          c / 2 = v /[1-(v^2/c^2)]         On simplificationgives                          v =0.5c

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