A muon formed high in Earth\'s atmosphere travels towards Earth at a speed v = 0

Question

A muon formed high in Earth's atmosphere travels towards Earth at a speed v = 0.97c for a distance of 4.1 km as measured by an observer at rest with respect to Earth. It then decays into an electron, a neutrino, and an antineutrino (

A muon formed high in Earth's atmosphere travels towards Earth at a speed v = 0.97c for a distance of 4.1 km as measured by an observer at rest with respect to Earth. It then decays into an electron, a neutrino, and an antineutrino (mu rightarrow e- + v + v). How long does the muon survive according to an observer at rest on Earth? Compute the gamma factor associated with the muon. How much time passes according to an observer traveling with the muon? What distance does the muon travel according to an observer traveling with the muon?

Explanation / Answer

Part A)

Apply d = vt

4100 = (.97)(3 X 10^8)(t)

t = 1.41 X 10^-5 sec which is 14.1 us

Part B)

Gamma = 1/sqrt(1 - v^2/c^2) = 1/sqrt(1 - .97^2)

Gamma = 4.11

Part C)
T = (1/4.11)(T')

T = (1/4.11)(14.1)

T = 3.43 us (3.43 X 10^-6 sec)

Part D)
d = vt

d = (.97)(3 X 10^8)(3.43 X 10^-6)

d = 997 m

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