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In the reference frame K a muon moving w...

In the reference frame K a muon moving with a velocity `v=0.990c` travelled a distance `l=3.0km` 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".

Text Solution

Verified by Experts

(a) If `tau_0` is the proper life time of the muon the life time in the moving frame is
`(tau_0)/(sqrt(1-v^2//c^2))` and hence `l=(vtau_0)/(sqrt(1-v^2//c^2))`
Thus `tau_0=l/vsqrt(1-v^2//c^2)`
(The words "from the muon's stand point" are not part of any standard terminology)
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