Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has a velocity v = 0.950c. The muon then travels at constant velocity and lives 1.52 μs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.) How long does the muon live as measured by an Earth-bound observer? (See Figure 28.7.)

Strategy

A clock moving with the system being measured observes the proper time, so the time we are given is Δt₀ = 1.52 μs. The Earth-bound observer measures At as given by the equation Δt=yΔt₀. Since we know the velocity, the calculation is straightforward.

Transcribed Image Text:

At At μ V