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Muons are elementary particles with a small mass. They are often created in the atmosphere by...

Muons are elementary particles with a small mass. They are often created in the atmosphere by cosmic ray collisions. Once the muon is created, its lifetime is only 2 microseconds (2×10−6 seconds). A typical velocity is 0.9999 c, just 0.1 % below the speed of light. Without relativity, the muons would only travel 600 meters before decaying, yet we see muons created 10 km in the air reach our instruments on the ground.

a) Consider a muon created 10km above the Earth’s surface (in the frame of the Earth) which travels directly towards the Earth’s surface. How much time, as seen from the Earth, does the muon take to reach the ground?

b) What is the proper time experienced by the muon before it reaches the ground (the time experienced by the muon)?

c) What is the distance traveled from the muon’s creation until it reaches the surface of the Earth in the muon’s frame?

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