1. The problem statement, all variables and given/known data A particle and its anti-particle are directed toward each other, each with rest energy 1,000 MeV. We want to create a new particle with rest energy 10,000 MeV and total energy 100,000 MeV. What must the speed of the particle and antiparticle be before the collision. ERest0 = m0c2 = 1,000 MeV ERestFinal = 10,000 MeV ETotal = 100,000 MeV 2. Relevant equations γx = 1 / √[1 - (vx2 / c2)] Conservation of Energy: EInitial = EFinal Conservation of Momentum: PInitial = PFinal Total energy: ETotal = √[(pc)2 + (ERest)2] ETotal = ERestγ Relativistic Momentum for the particles: PInitial = m0 / c2 * [v1γ1 + v2γ2] Solving for momentum in terms of the total and rest energies: PFinal = 1 / c * √[(ET)2 - (ERestFinal)2] 3. The attempt at a solution First I laid out conservation of energy. EInitial = EFinal ERest0[γ1 + γ2] = 100,000 MeV 100 = γ1 + γ2 Then I solved for the final momentum using the expression above which is derived from the total energy formula. PFinal = 1 / c * √[(100,000)2 + (10,000)2] PFinal = 1 / c * 99,498 MeV The I setup conservation of momentum. PFinal = PInitial 1 / c * 99,498 MeV = m0 / c2 * [v1γ1 + v2γ2] 1 / c * 99,498 MeV / [1,000 MeV / c2] = [v1γ1 + v2γ2] 99.498c = [v1γ1 + v2γ2] This is where I get stuck. I don't know whether I should attempt to solve for one of the velocities or just in general which step to take next. I tried solving by setting one of the velocities to zero but I'm not sure if this is the correct way to do it. If I substitute v2 = 0: γ2 = 1 100 = γ1 + 1 99 = γ1 √[1-(v12 / c2)] = 1 / 99 v12 / c2 = 1 - (1 / 99)2 v1 = √[1 - (1 / 99)2] c v1 = .99995c Is this answer right? v1 = .99995c and v2 = 0c Can someone please either verify my answer or give me a step in the right direction? Thank you.