Walker, Halliday & Resnick — Relativity: Problem 38

38 A rod is to move at constant speed \( v \) along the \( x \) axis of reference frame \( S \), with the rod’s length parallel to that axis. An observer in frame \( S \) is to measure the length \( L \) of the rod. Figure 37-17 gives length \( L \) versus speed parameter \( \beta \) for a range of values for \( \beta \). The vertical axis scale is set by \( L_a = 1.00 \text{ m} \). What is \( L \) if \( v = 0.90c \)?