A muon is created 53.0km above the surface of the earth (as measured in the eart

Question

A muon is created 53.0km above the surface of the earth (as measured in the earth's frame). The average lifetime of a muon, measured in its own rest frame, is 2.20s , and the muon we are considering has this lifetime. In the frame of the muon, the earth is moving toward the muon with a speed of 0.983c.

A)In the muon's frame, what is its initial height above the surface of the earth?

B) In the muon's frame, how much closer does the earth get during the lifetime of the muon?

C) What fraction is this of the muon's original height, as measured in the muon's frame?

D) In the earth's frame, what is the lifetime of the muon?

E)In the earth's frame, how far does the muon travel during its lifetime?

F)What fraction is this of the muon's original height in the earth's frame?

Explanation / Answer

The Lorentz factor at 0.989c = sqrt(1/(1-v2/c2)) = 6.76

a) (58.0/6.76) km = 8.58 km

b) (2.20 * 10-6 s)(0.989 * 2.9979 * 108 m/s) = 652 m

c) = 652/8580 = 7.60%

d) (2.20 * 10-6 s)*(6.76) = 1.49 * 10-5 s

e) (1.49 * 10-5 s)(0.989 * 2.9979 * 108 m/s) = 4410 m

f) 4410/58000 = 7.60% , exactly the same as the other reference frame and thus perfectly consistent.

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