1.(i) A muon decays with a mean lifetime of 2.2010^(-6) s as measured in a frame

Question

1.(i) A muon decays with a mean lifetime of 2.2010^(-6) s as measured in a frame of reference in which it is at rest. If a muon is moving at 0.990c relative to the earth. What will you (an observer from earth) measure its mean lifetime to be? (ii) Grady boards a spaceship, and then zips past Jameson on Earth at a relative speed of 0.600c. At the instant Grady passes, both start timers. (a) At the instant when Jameson measures that Grady has traveled 9.0010^7 m past him, what does Grady’s timer read? (b) At the instant when Grady reads 0.400 s on his timer, what does Jameson read on his?

Explanation / Answer

(i) t = t' / (1 - v2/c2)1/2 = 2.20 * 10-6 / (1 - 0.9902)1/2 = 1.56 * 10-5 s

(ii) a) Time passed according to Jameson, t = (9 * 107) / (0.6 * 3 * 108) = 0.5 s

Time passed according to Grady, t' = t(1 - v2/c2)1/2 = 0.5 * (1 - 0.62)1/2 = 0.4 s

b) t = t' / (1 - v2/c2)1/2 = 0.4 / (1 - 0.62)1/2 = 0.5 s

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