
(a)
Does the muon reach Earth's surface within one half-life if Muons have a proper half-life of

Answer to Problem 77QAP
The muon does not make it to Earth
Explanation of Solution
Calculation:
Muons have a proper lifetime of
Length contraction in the muon's reference frame:
Distance traveled by the muon in the muon's reference frame:
Because 444.6 m <937 m, the muon does not make it to Earth.
Time dilation in Earth's reference frame:
Distance traveled in Earth's reference frame:
Because 1425 m <3000 m, the muon does not make it to Earth.
Conclusion:
The muon does not make it to Earth
(b)
The minimum speed of the muon so that it just barely reaches Earth's surface after one half-life?

Answer to Problem 77QAP
The minimum speed = 0.988c
Explanation of Solution
Calculation:
The minimum speed = 0.988c
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Chapter 25 Solutions
COLLEGE PHYSICS
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