Muons created at rest in the laboratory are found to have a meanlifetime of 2s a

Question

Muons created at rest in the laboratory are found to have a meanlifetime of 2s and the
average height of the outer edge of earth’s atmosphere is103km. Hint: Keep at least 6 decimal
places in your calculations. More is better in this case.
a) In order for a muon created in the upper atmosphere to reach theplanetary surface, what
relative velocity must it have? Express your answer as a fractionof c
b) How long does the trip take in the muon reference frame? Is thisa proper time? Explain.
c) Determine the atmosphere thickness in the muon reference frame.Is this a proper length?
Explain.

LIFESAVER rating will be awarded if youshow ALL WORK, and explain your reasoning.

Explanation / Answer

let the muon speed be v = c the gamma factor is = 1/(1-2) > 1 in earth frame, flight time is dilated to t = (2 x 10-6) = 103000/v = 103000/(c)= .000343333/ solving for , = .999983 v = .999983 c in muon rest frame, this takes 2 s. in muon reference frame, the atmospheric thickness iscontracted as d = 103000/ = 600.6 m

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