Physics Practice Problems Consequences of Relativity Practice Problems Solution: Muons are commonly produced in the upper atmospher...

Solution: Muons are commonly produced in the upper atmosphere due to collisions of cosmic rays with the atoms in the atmosphere. The muons produced commonly travel downwards at speeds up to 0.99 c. If the half life of the muon, in the rest frame, is 2.2 μs, (a) How long is the muon's half life, according to an observer at rest on the Earth's surface (b) How far can the muon travel, according to an observer at rest on the Earth's surface?

Problem

Muons are commonly produced in the upper atmosphere due to collisions of cosmic rays with the atoms in the atmosphere. The muons produced commonly travel downwards at speeds up to 0.99 c. If the half life of the muon, in the rest frame, is 2.2 μs,

(a) How long is the muon's half life, according to an observer at rest on the Earth's surface

(b) How far can the muon travel, according to an observer at rest on the Earth's surface?