# Find total E of muon using time dilation

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

An Ω particle has rest energy 1672 MeV and mean lifetime 8.2*1011 s. It is created and decays in a particle track detector and leaves a track 24 mm long. What is the total energy of the particle?

2. Relevant equations

E=$\frac{mc^2}{\sqrt{1-(\frac{v}{c})^2}}$

t=t0$\sqrt{1-(\frac{v}{c})^2}$

Rest E=mc2

3. The attempt at a solution

Because Rest E=mc2 I know that:

E=$\frac{1672 MeV}{\sqrt{1-(\frac{v}{c})^2}}$

What I need to do now is solve for v using the given time and distance (.024 meters). The time is measured in the particle’s proper frame so:

t=(8.2*1011 seconds)$\sqrt{1-(\frac{v}{c})^2}$

Of course, this contains v itself. What am I missing?

Thank you!

http://ift.tt/1c2VeLH