Time Dilation: Muon Lifetime · USAPhO 2020 #6

Physics · special-relativity

Problem

Muons (

\tau_0 = 2.2\;\mu\text{s}

) are created at the top of the atmosphere (

h = 10\;\text{km}

) moving at

v = 0.995c

. What fraction of muons survive to reach the ground? (In the muon frame, use length contraction; in the Earth frame, use time dilation.)