27. Particles called muons are constantly being created by high-energy collisions in the upper atmosphere. Suppose...

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27. Particles called muons are constantly being created by high-energy collisions in the upper atmosphere. Suppose a muon covers 100,000 m from the upper atmosphere to a detector on Earth, traveling at 99.999% of the speed of light. (a) A muon at rest in a lab typically decays after 2.2 10-6 seconds. Show that, according to non-relativistic calculations, the muon will not reach the detector. (b) But in fact, most of the muons created at that height do make it to Earth. Show how relativis- tic calculations explain why. 27. Particles called muons are constantly being created by high-energy collisions in the upper atmosphere. Suppose a muon covers 100,000 m from the upper atmosphere to a detector on Earth, traveling at 99.999% of the speed of light. (a) A muon at rest in a lab typically decays after 2.2 10-6 seconds. Show that, according to non-relativistic calculations, the muon will not reach the detector. (b) But in fact, most of the muons created at that height do make it to Earth. Show how relativis- tic calculations explain why.