What is the Relative Momentum of Two Particles After Collision?

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Homework Statement




A particle of mass m and momentum of magnitude 2mc strikes a particle of mass m, which is at rest. The two particles stick together after collision. c represents the speed of light.

(a) Before the collision, the ratio of the speed of the moving particle to the speed of light is

(b) After the collision, the ratio of the magnitude of total momentum to mc is

(c) After the collision, the ratio of the speed of the two particles to the speed of light is


Homework Equations



p = mv\gamma

vi/c = \frac{2}{\sqrt{5}}

The Attempt at a Solution



Since both particles stick together, their mass is 2m and their momentum is 2mvf\gamma

the initial momentum is mvi\gamma.

Set both of these equations equal to each other, and solve for vf/c which is:

\frac{1}{\sqrt{5}}.

It's not the right answer though. Anyone tell me what I did wrong?
 
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