A particle of rest mass m and kinetic energy 2mc^c strikes and sticks to a stationary particle of rest mass 2m. Find the rest mass M of the composite particle
E = mc^2 + KE
E^2 = (mc^2)^2 + (pc)^2
p = mv/sqrt(1-v^2/c^2)
The Attempt at a Solution
For finding the initial velocity of the moving particle:
2mc^2 = KE = mc^2/sqrt(1-v^2/c^2) - mc^2
and when solving for v, you get v1 = sqrt(2/3)c
To find M, I tried using conservation of momentum and energy.
p1 = p2
mv1/sqrt(1-v1^2/c^2) + 2m*0 = Mv2/sqrt(1-v2^2/c^2)
I can't seem to find a way to make the equation only have one unknown.