Introduction to Classical Mechanics · Problem 11.39
Relativity (Kinematics) — Morin
Physics — Mechanics · twice-simultaneous
Problem
A train of proper length L moves at speed v with respect to the ground. When the front of the train passes a tree on the ground, a ball is simultaneously (as measured in the ground frame) thrown from the back of the train toward the front, with speed u with respect to the train. What should u be so that the ball hits the front simultaneously (as measured in the train frame) with the tree passing the back of the train? Show that in order for a solution for u to exist, we must have v/c<(5−1)/2, which happens to be the inverse of the golden ratio.