Relativity and energy (think its dead easy, I just can't see it)

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The discussion revolves around calculating the total energy and momentum of a system consisting of a proton with 2 GeV of energy and a photon with 50 MeV traveling at a 45-degree angle. The user correctly sums the energies, arriving at a total energy of 2.05 GeV. They question whether direction needs to be considered in their calculations. The momentum equations are outlined, confirming that the x-component of momentum includes contributions from both the proton and photon, while the y-component only includes the photon. The conversation highlights the importance of understanding energy and momentum conservation in relativistic contexts.
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Homework Statement


A proton has total energy 2GeV and is traveling along the x-axis. A photon with energy 50MeV travels at an angle of 45 degrees to this axis. What is the total energy and momentum of the system?


Homework Equations


Non-really


The Attempt at a Solution


Total E = 2Gev + 50 MeV = 2.05GeV yes? I don't need to take any directions into account here do I?

Then px = p(proton) + px(photon), and py = py(photon) yes?
 
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