How thick is the atmosphere in the rest frame of a high-energy muon?

[nn542]

Homework Statement

a muon(mass 106 MeV/c^2)is produced in the upper atmosphere with an energy of 10000MeV. The Earth's atmosphere is 100km thick.In the rest frame of the muon, how thick is the atmosphere?

Homework Equations

E^2=P^2c^2+m^2c^4(I don't know what equation to put here. I think I have to use the equation of relativity.)

The Attempt at a Solution

the answer is 1.06km

I'm wondering how to calculate the velocity of muon?~~

 

[Simon Bridge]

The thickness of the atmosphere has dimensions of what?
In relativity you get
1. time dilation
2. length contraction
... which do you think is needed here?

You don't need the speed of the muon, just the gamma factor.
Get it from the total energy: $E=\gamma mc^2$