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Relativistic Mechanics

Problem 1.347

In the reference frame KK a muon moving with a velocity v=0.990cv=0.990 c travelled a distance l=3.0 kml=3.0 \mathrm{~km} from its birthplace to the point where it decayed. Find: (a) the proper lifetime of this muon; (b) the distance travelled by the muon in the frame KK "from the muon's standpoint".

Reveal Answer
1.347. (a) Δt0=(l/v)1−(v/c)2=1.4μ\Delta t_{0}=(l / v) \sqrt{1-(v / c)^{2}}=1.4 \mu; (b) l′=l1−(v/c)2=0.42 kml^{\prime}=l \sqrt{1-(v / c)^{2}}=0.42 \mathrm{~km}
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