Halliday, Resnick & Walker — Relativity: Problem 44

44 Bullwinkle in reference frame \(S'\) passes you in reference frame \(S\) along the common direction of the \(x'\) and \(x\) axes, as in Fig. 37-9. He carries three meter sticks: meter stick 1 is parallel to the \(x'\) axis, meter stick 2 is parallel to the \(y'\) axis, and meter stick 3 is parallel to the \(z'\) axis. On his wristwatch he counts off 10.0 s, which takes 30.0 s according to you. Two events occur during his passage. According to you, event 1 occurs at \(x_1 = 33.0\text{ m}\) and \(t_1 = 22.0\text{ ns}\), and event 2 occurs at \(x_2 = 53.0\text{ m}\) and \(t_2 = 62.0\text{ ns}\). According to your measurements, what is the length of (a) meter stick 1, (b) meter stick 2, and (c) meter stick 3? According to Bullwinkle, what are (d) the spatial separation and (e) the temporal separation between events 1 and 2, and (f) which event occurs first?