A muon has a mean proper lifetime

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics

Relativity and Gravitation, Ch Time dilation, length contraction and simultaneity

Problem

\tau_0 = 2.20\ \mu\mathrm{s}

, the mean lifetime read by a clock travelling with it. In the ground frame

S

the muon moves in a straight line along the

+x

axis at the constant speed

v = 0.950c

, with

c = 2.998\times10^8\ \mathrm{m\,s^{-1}}

. The muon rest frame

S'

is in standard configuration with

S

; both frames are inertial and air resistance and gravity are ignored. ((a)) What is the mean lifetime of such muons as measured in the ground frame

S

? ((b)) Two marker lamps stand on the ground

1.20\ \mathrm{km}

apart along

x

as measured in

S

. How far apart are they as measured in the muon frame

S'

? ((c)) The two lamps flash simultaneously in

S

. What is the magnitude of the time interval between the two flashes as measured in the muon frame

S'

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