For the passing reference frames in Figure events A and B occur at the following space time coordinates: according to the unprimed frame, (xA, tA) and (xB, tB); according to the primed frame, (xA, tA) and (xB, tB).In the unprimed frame, Δ t = tB ?? tA = 1.00μs and Δx = xB ?? xA = 400 m.

(a) Find an expression for Δx' in terms of the speed parameter β and the given data. Graph Δx' versus β for two ranges of β:

(b) 0 to 0.01 and

(c) 0.1 to 1.

(d) At what value of β is Δx' minimum,?

Event Unprimed Primed (xA, tA) (Xg, Ig) (xA, t) (rg, tB) x" A XA (a) Event A (b) Event B