Question

» Problem 2-13: Consider a muon traveling straight down towards the surface of the Earth at Lorentz fac- tor γι ~ 18.8. (a) What is the vertical distance between Denver and Echo Lake, according to the muon? (b) How long does it take the muon to traverse this distance, ac- cording to the muon? (c) What is the muon's mean life- time, according to the muon? (d) Answer the above parts again but now for a muon traveling at Lorentz factor 12 6.3.

Answer 1

(a)

$\gamma_1=\frac {1}{\sqrt {1-\frac {v^2}{c^2}}}$

$18.8=\frac {1}{\sqrt {1-\frac {v^2}{c^2}}}$

$v=0.998 \ c$

$d=\frac {d_0}{\gamma_1}=\frac {1600}{18.8}\: m= 85.10\: m$

(b)

$t=\frac {d}{v}=\frac {85.10}{0.998\cdot 3\cdot 10^8}\: s= 2.84\times 10^{-7}\: s$

(c)

$t_0=\frac {t}{\gamma}=\frac {2.84\cdot 10^{-7}}{18.8}=1.51\times 10^{-8}\:s$

(d)

Can be done as done in the earlier parts.