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## Homework Statement

A particle of rest mass m

_{0}moving at a speed of 3/4 c collides with a same-mass particle at rest and they stick together to form a composite particle. What is the rest mass of the composite particle and what is its speed?

## Homework Equations

[tex]E = \gamma mc^2[/tex]

[tex]p = \gamma mu[/tex]

[tex]\gamma = \frac{1}{\sqrt{1- \beta ^2}}[/tex]

## The Attempt at a Solution

So far I have written out equations for initial energy and momentum and final energy and momentum. I rearranged both for [itex]\beta_{final}[/itex] and set them equal, with the aim of solving for [itex]v_{final}[/itex]. I got a velocity which was larger than the velocity of the initial particle which surely can't be right.

I won't write out all my workings as it would take an age but here is what I got for [itex]\beta_{final}[/itex] for the energy equation after cancelling/simplifying:

[tex]\beta_{final} = -3 -4 \beta_{initial} ^2[/tex]

And for the momentum equation:

[tex]\beta_{final} = 1 - \frac{(4 v_{final} ^2)(1 - \beta_{initial} ^2)}{v_{initial} ^2}[/tex]

As I said, I then set them equal and solved for [itex]v_{final}[/itex]. Any ideas?

Cheers!

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