Question

Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.915c. The muon then travels at constant speed and lives 1.35 μs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.)

a)  How many kilometers does the muon travel according to an observer moving with the muon? Call this d_m.

b)  For how long does the muon live according to an Earth-bound observer? Give your answer in μs.

c)  How many kilometers does the muon travel according to an Earth-bound observer? Call this d_E.

d) Write an expression relating the answer to part (c) to the answer in part (a). That is to say, write d_E in terms of d_m, v, and the speed of light, c.

e) Given the mass of a muon is m = 1.88 × 10^-28 kg, what is the kinetic energy of this muon traveling toward Earth, as measured by an observer on Earth? Giver your answer in joules.

f) During the muon's flight, a signal on Earth's surface blinks on and then off. An observer on Earth measures that the signal light was on for t_s = 2.2 μs. What is the duration of the signal light as measured by an observer moving with the muon? Give your answer in μs.

g) A second muon is also produced and travels along the same line as the first one with a speed of v₂ = 0.51c as measured by an observer on Earth. What is the velocity of this second particle relative to the the first muon? Give your answer in terms of the speed of light, c.

Answer 1