Relativistic Momentum of a particle

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The discussion revolves around calculating the unknown mass M of a particle that decays into two known masses, m1 and m2, with specified momenta. The user attempts to apply the Pythagorean theorem to sum the momenta but seeks clarification on the underlying principles. The key to solving the problem lies in using conservation of momentum and energy principles to derive the velocity in the ground frame. The conversation emphasizes the importance of these conservation laws in particle decay scenarios. Ultimately, understanding these concepts is crucial for accurately determining the unknown mass and speed of the original particle.
~Sam~
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Homework Statement


A particle of unknown mass M decays into two particles of known masses m1 = 0.5 GeV/c2 and m2 = 1.0 GeV/c2, whose momenta are measured to be p1 = 2.0 GeV/c along the positive y-axis and p2 = 1.5 GeV/c along the positive x-axis. Find the unknown mass M and its speed.


Homework Equations



p=1/sqrt(1-v^2/c^2)(mu)

The Attempt at a Solution



I tried summing the momentas, via pythagoras theorem. after that I'm not sure.
 
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What's the general principle which governs how you can find the answer? I.e. for a given mass 'M,' why wouldn't m1 = 500000 GeV and m2 = 100000 Gev?

Hint: what if you think about the decay reaction as a collision?
 
Ahh I got it...using conservation of energy.
 
use conservation of momentum and energy to get the velocity in ground frame
 

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