Alice, an inertial observer, see Bob undergoing hyperbolic motion given by the parametric equations z0(1) = %Sinh L, z(r)= %cosh Z in her frame. a) Using an appropriate Lorentz transform with Bob's coordinates taken as primed coordinates, show by taking the differentials of the parametric equations, that A7 = A', that is, that 7 is Bob's proper time, and that his rapidity is % . b) Transform the differentials Az and Az you calculated in part a) to primed coordinates to reinforce the correctness of part a) calculation. c) Taylor expand to second order in AT the results for Az? and Az to provide the physical interpretation of the parameter g. (This is the grown-up version of Problem 12.28))