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

AI Thread Summary
To determine the thickness of the atmosphere in the rest frame of a high-energy muon, the relevant factors include the muon's energy and the effects of relativity, specifically length contraction. Given that the muon has an energy of 10,000 MeV and a mass of 106 MeV/c^2, the gamma factor can be calculated using the total energy equation E = γmc^2. The thickness of the atmosphere in the muon's rest frame is found to be approximately 1.06 km. Understanding time dilation and length contraction is essential for solving this problem, but only the gamma factor is necessary for the calculation. The discussion emphasizes the importance of relativity in determining the perceived thickness of the atmosphere from the muon's perspective.
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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?~~
 
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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##
 

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