The Cosmic Ray Muon Detector · AI Generator #GEN-BAEE13EC
Physics · modern-physics
Problem
A high school physics class builds a cosmic ray detector to study muons created when cosmic rays hit the upper atmosphere. Muons are created at an altitude of approximately 15km and travel downward at 0.95c toward the detector on the ground. At rest, muons have a proper lifetime of τ0=2.2×10−6s before they decay.
(a) Without considering relativistic effects, what fraction of the original muons would survive the journey to reach the ground-based detector?
(b) Taking into account time dilation, what fraction actually survives to reach the detector?
(c) The students measure that their detector registers 450 muons per hour. Estimate how many muons per hour were originally created in the 15km column of atmosphere directly above their detector.