Walker, Halliday & Resnick — Relativity: Problem 56

56 Inertial frame \( S' \) moves at a speed of \( 0.65c \) with respect to frame \( S \) (Fig. 37-9). Further, \( x = x' = 0 \) at \( t = t' = 0 \). Two events are recorded. In frame \( S \), event 1 occurs at the origin at \( t = 0 \) and event 2 occurs on the \( x \) axis at \( x = 3.0 \text{ km} \) at \( t = 4.0 \text{ }\mu\text{s} \). According to observer \( S' \), what is the time of (a) event 1 and (b) event 2? (c) Do the two observers see the same sequence or the reverse?