Relativity question

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Homework Statement



http://img140.imageshack.us/img140/1650/25406466.jpg [Broken]

Homework Equations



[tex]E^{2}= (pc)^{2}+m_{0}^{2}c^{4}[/tex]

The Attempt at a Solution



To find the energy I said that in the rest frame of the pion, it has energy 139.6Mev, so this has to equal the sum of the energies of the decay products. I then used conservation of momentum to find an equation for the energy of the muon:

[tex]E_{1}=\frac{139.6^2+105.7^2}{2*139.6} Mev = 109.8 Mev [/tex].

And so the energy of the neutrino is

[tex]E_{2}=139.6-109.8 Mev = 29.8 Mev [/tex].

I think these are correct. You can the rest energies from these total energies to get the kinetic energies of each:

[tex]KE_{1} = 109.8-105.7 Mev = 4.1 Mev [/tex]
[tex]KE_{2} = 29.8 Mev [/tex].

The momentum can be calculated by rearranging the equation for [tex]E^{2}[/tex] given above, and I found

[tex]p_{1} = 29.7 Mev/c[/tex]
[tex]p_{2} = 29.8 Mev/c[/tex] .

Hopefully those are all okay. I'm unsure as to how to find the speed with respect to c though. If I rearrange the equation for kinetic energy in order to find v, what is this v with respect to?

Thanks.
 
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