Chapter 37, Problem 61P

Spatial separation between two events. For the passing reference frames of Fig. 37-25, events A and B occur with 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, Δt = t_B − t_A = 1.00 µs and Δx = x_B − x_A = 240 m. (a) Find an expression for Δx' in terms of the speed parameter ß and the given data. Graph Ax'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 Δx' = 0?