Walker, Halliday & Resnick — Relativity: Problem 47

47 In Fig. 37-9, the origins of the two frames coincide at \(t = t' = 0\) and the relative speed is \(0.980c\). Two micrometeorites collide at coordinates \(x = 100 \text{ km}\) and \(t = 200 \text{ }\mu\text{s}\) according to an observer in frame \(S\). What are the (a) spatial and (b) temporal coordinate of the collision according to an observer in frame \(S'\)?