Ch26 Relativity A muon formed high in Earth\'s atmosphere travels towards Earth
ID: 1787091 • Letter: C
Question
Ch26 Relativity A muon formed high in Earth's atmosphere travels towards Earth at a speed v-020c for a d. 15 points SerCP10 26.P.007 My Notos Ask Your Teache A muon formed high in Earth's atmosphere travels towards Earth at a speed v = 0.920c for a distance of 3.70 km as measured by an observer at rest with respect to Earth. It then decays into an electron, a neutrino, and an antineutrino. (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 with the muon? ) What distance does the muon travel according to an observer traveling with the muon? (e) A third observer traveling toward the muon at c/2 measures the lifetime of the particle. According to the observer, is the muon's lifetime shorter or longer than the lifetime measured by the observer at rest with respect to Earth? Explain This answer has not been graded yet. eed Help?Read itExplanation / Answer
The proper time t' applies to the muon's reference frame.
So:
t = t’/ [1 - v^2/c^2]^ ½
and t' = t [1 - v^2/c^2]^ ½
v = 0.92 c and v^2 = (0.92c)^2 = 0.85c^2
Then: t' = t [1 - 0.85c^2/c^2]^ ½ = t [0.15]^ ½ = t(0.387)
recall distance travelled = 3.7 km = 3700 m
To get t' we need to find t first, e.g.
t = 3700m/ (2.97 x 10^8 m/s) = 1.25 x 10^-5 s
Then: t' = (1.25 x 10^-5 s) (0.387) = 3.23 x 10^-5 s
The distance traveled in its frame is just the proper length, L'
so:
L' = 3700 m [[1 - v^2/c^2]^ ½ = 3700m (0.15)^ ½
L' = 3700 m (0.387) = 1431.9 m