Chapter 37, Problem 22P

For the passing reference frames in Fig. 37-25, events A and B occur at the following spacetime coordinates: according to the unprimed frame, (x_A, t_A) and (x_B, t_B); according to the primed frame, (x'_A, t'_A) and (x'_B, t'_B). In the unprimed frame, ∆t = t_B − t_A = 1.0 µs and Δx = x_B − x_A = 400 m. (a) Find an expression for ∆x' in terms of the speed parameter ß and the given data. Graph ∆x' versus ß for two ranges of ß: (b) 0 to 0.01 and (c) 0.1 to 1. (d) At what value of ß is ∆x' minimum, and (e) what is that minimum?