Suppose a cosmic ray colliding with a nucleus in the Earth\'s upper atmosphere p

Question

Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.89c. The muon then travels at constant speed and lives 1.5 mu s as measured in the muon's frame of reference (You can imagine this as the muon's internal clock.) Randomized Variables v = 0.89 c t = 1.5 mu s How many kilometers does the muon travel according to an Earth-bound observer? How many kilometers of the Earth pass by as viewed by an observer moving with the muon? Base your calculation on its speed relative to the Earth and its lifetime (proper time).

Explanation / Answer

L = v*t = 0.89*3*10^8 *1.5*10^-6 = 400.5

b.) L = Lo( sqrt(1 -V^2/c^2))

L = 182.612 m

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