Suppose a muon produced as a result of a cosmic ray colliding with a nucleus in

Question

Suppose a muon produced as a result of a cosmic ray colliding with a nucleus in the upper atmosphere has a velocity v = 0.950c. Suppose it travels at constant velocity and lives 2.20 mu s 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 mu s as measured by an Earth-bound observer. (a) How long (in mu s) would the muon have lived as observed on Earth if its velocity was 0.525c? What is time dilation? What is the gamma factor? Can you simplify it by canceling c? (b) How far (in m) would it have traveled as observed on Earth? (c) What distance (in m) is this in the muon's frame? How far does the muon travel as measured by an observer traveling with it at the same speed?

Explanation / Answer

Using:

a) t = t0 gamma = 2.20/sqrt(1-0.525^2)=2.58 us

b) d = v t = 0.525*3*10^8*2.58*10^-6=406.35 m

c) length contraction:

=406.35*sqrt(1-0.525^2)=345.84 m

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