# Relativity question

1. Mar 30, 2009

### kidsmoker

1. The problem statement, all variables and given/known data

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

2. Relevant equations

$$E^{2}= (pc)^{2}+m_{0}^{2}c^{4}$$

3. 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:

$$E_{1}=\frac{139.6^2+105.7^2}{2*139.6} Mev = 109.8 Mev$$.

And so the energy of the neutrino is

$$E_{2}=139.6-109.8 Mev = 29.8 Mev$$.

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

$$KE_{1} = 109.8-105.7 Mev = 4.1 Mev$$
$$KE_{2} = 29.8 Mev$$.

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

$$p_{1} = 29.7 Mev/c$$
$$p_{2} = 29.8 Mev/c$$ .

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.

Last edited by a moderator: May 4, 2017