Introduction to Classical Mechanics · Problem 11.42
Relativity (Kinematics) — Morin
Physics — Mechanics · tunnel-fraction
Problem
A person runs with speed v toward a tunnel of length L. A light source is located at the far end of the tunnel. At the instant the person enters the tunnel, the light source simultaneously (as measured in the tunnel frame) emits a photon that travels down the tunnel toward the person. When the person and the photon eventually meet, the person's location is a fraction f along the tunnel. What is f? Solve this by working in the tunnel frame, and then again by working in the person's frame.