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Suppose a muon produced as a result of a cosmic ray colliding with a nucleus in the upper atmosphere has a velocity v = 0.9500c. Suppose it travels at constant velocity and lives 1.52 µs as measured by an observer who moves with it (this is the time on the muon's internal clock). It can be shown that it lives for 4.87 µs as measured by an earth-bound observer (see Example 26.1 in the textbook). Give all answers correct to 4 significant figures.

(a) How long would the muon have lived as observed on earth if its velocity was 0.0700c?

(b) How far would it have traveled as observed on earth?

(c) What distance is this in the muon's frame?

Explanation / Answer

a) t = t0 gamma = 1.52/sqrt(1-0.07^2)=1.5237 us

b) d = v t = 0.07*3.0E8*1.5237E-6=31.997 m

c) length will be contracted 31.997*sqrt(1-0.07^2)=31.92 m

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