Suppose a cosmic ray colliding with a nucleus in the Earth'supper atmosphere produces a muon that has speed v =0.915c. The muon then travels at constant speed and lives1.35 μs as measured in the muon's frame of reference. (You canimagine this as the muon's internal clock.)
a)Â Â How many kilometers does the muon travel accordingto an observer moving with the muon? Call thisdm.
b)  For how long does the muon live according to anEarth-bound observer? Give your answer in μs.
c)Â Â How many kilometers does the muon travel accordingto an Earth-bound observer? Call this dE.
d) Write an expression relating the answer to part (c) to theanswer in part (a). That is to say, write dE interms of dm, v, and the speed oflight, c.
e) Given the mass of a muon is m = 1.88 ×10-28 kg, what is the kinetic energy of this muontraveling toward Earth, as measured by an observer on Earth? Giveryour answer in joules.
f) During the muon's flight, a signal on Earth's surface blinkson and then off. An observer on Earth measures that the signallight was on for ts = 2.2 μs. What is theduration of the signal light as measured by an observer moving withthe muon? Give your answer in μs.
g) A second muon is also produced and travels along the sameline as the first one with a speed of v2 =0.51c as measured by an observer on Earth. What is thevelocity of this second particle relative to the the first muon?Give your answer in terms of the speed of light, c.
