All Problems Relativistic Mechanics
Problem 1.347
In the reference frame \(K\) a muon moving with a velocity \(v=0.990 c\) travelled a distance \(l=3.0 \mathrm{~km}\) 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 \(K\) "from the muon's standpoint".
1.347. (a) \(\Delta t_{0}=(l / v) \sqrt{1-(v / c)^{2}}=1.4 \mu\); (b) \(l^{\prime}=l \sqrt{1-(v / c)^{2}}=0.42 \mathrm{~km}\)