[填空题]
a. A muon is created in a high-energy cosmic ray interaction in Eartylht x,4ye*+2w1cra gh’s )kxk - 8:wn ,zzswn+4hmu/h mfupper atmosphere. Th4k+ wsm uhm )kzwn -,/n8fxhz:e lifetime of the muon before decay is $2.3 \times 10^{-6} \, s$ in its frame of reference. The lifetime of the muon is measured as $11 \times 10^{-6} \, s$ from the perspective of an observer on Earth.
i. State and explain which of the given lifetimes is the proper time.
ii. Calculate, according to the theory of special relativity, the speed of the muon is around % of the speed of light.
iii. Muons are likely created at $10 \, km$ above the earth’s surface. Most of the muons are detected on the surface of the Earth. Explain how this observation can be interpreted as proof of special relativity.
b. A space-time diagram shows a motion of a muon in the frame of reference of a stationary observer at the place where the muon is created.
i. By using the information in a.(ii), calculate the angle $θ$ shown on the graph. $\theta$ = $^{\circ}$
ii. Another muon is created a few kilometres below the muon in b.(i) at the same time. It is moving at $0.75$c. Draw the worldline of the second muon on the graph in b.(i) according to the same observer.
