(a) How long would the muon in Example 28.1 have lived as observed on the Earth if...
Question:
(a) How long would the muon in Example 28.1 have lived as observed on the Earth if its velocity was 0.0500c?
(b) How far would it have traveled as observed on the Earth?
(c) What distance is this in the muon's frame?
Data from Example 28.1
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 Δt as given by the equation Δt = γΔt0. Since we know the velocity, the calculation is straightforward.
Step by Step Answer:
a To solve this problem we can use the following equation t t0 where t is the time measured by the E...View the full answer
