Introduction to Classical Mechanics · Problem 11.41
Relativity (Kinematics) — Morin
Physics — Mechanics · photon-tree-and-house
Problem
(a) A train of proper length L moves at speed v with respect to the ground. At the instant the back of the train passes a certain tree, someone at the back of the train shines a photon toward the front. The photon happens to hit the front of the train at the instant the front passes a certain house. As measured in the ground frame, how far apart are the tree and the house? Solve this by working in the ground frame.
(b) Now look at the setup from the point of view of the train frame. Using your result for the tree--house distance from part (a), verify that the house meets the front of the train at the same instant the photon meets it.