A muon is created by a cosmic ray high in Earth\'s atmosphere. Ittravels towards

Question

A muon is created by a cosmic ray high in Earth's atmosphere. Ittravels towards Earth at a speed v = 0.93c for a distance of 4.7km as measured by an observer at rest with respect to Earth. Themuon is unstable, and decays (self-destructs) into 3 otherparticles after traveling this distance. (a) How long does the muonsurvive according to an observer at rest on Earth?
Enter anumber. 1 s

(b) Compute the value of gamma associated with the muon.
Enter anumber. 2

(c) How much time passes before the muon decays, according to anobserver traveling with the muon, i.e. in the rest frame of themuon?
Enter anumber. 3 s

(d) What distance does the muon travel before it decays, accordingto an observer traveling with the muon?
Enter anumber. 4 m
Enter anumber. Enter anumber. Enter anumber. Enter anumber.

Explanation / Answer

v=.93c d=4.7km=4.7x103m a.) t=d/v t=4.7x103m/.93(3x108m/s) t=1.64x10-5s b.)=1/(1-(v/c)2) =1/(1-(.93c/c)2) =1/(1-(.93)2) The "c" cancels. =2.72 c.) tp=t/ tp=1.64x10-5s/2.72 tp=6.03x10-6s d.)d=tv d=6.03x10-6s(.93(3x108m/s)) d=1.68m e.) The third person is moving opposite, so the speed is greaterthan the original making the muons life longer.

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