Halliday, Resnick & Walker — Relativity: Problem 46

Reference frame \(S'\) is to pass reference frame \(S\) at speed \(v\) along the common direction of the \(x'\) and \(x\) axes, as in Fig. 37-9. An observer who rides along with frame \(S'\) is to count off a certain time interval on his wristwatch. The corresponding time interval \(\Delta t\) is to be measured by an observer in frame \(S\). Figure 37-18 gives \(\Delta t\) versus speed parameter \(\beta\) for a range of values for \(\beta\). The vertical axis scale is set by \(\Delta t_a = 14.0\text{ s}\). What is interval \(\Delta t\) if \(v = 0.96c\)?