A muon formed high in Earth's atmosphere travels towards Earth at a speed v = 0.92c for a distance of4.2 km as gauged by an observer at rest by respect to Earth. It then decays into an electron, a neutrino, and an antineutrino (µ- e- + v +v).
a) How long does the muon survive according to an observer at rest on Earth?
b) Compute the gamma factor associated with the muon.
c) How much time passes according to an observer traveling by the muon?
d) What distance does the muon travel according to an observer traveling by the muon?
e) A third observer traveling toward the muon at c/2 measures the muon's lifetime shorter or longer than the lifetime gauged with the observer at rest with respect to Earth? Describe.