a) Inertial frame S' moves in the positive x direction relative to another inertial fran? S. The x' axis of S' is aligned with the x axis of S. Three observers, A, B and C. are at rest in S' and located at equal intervals along the x'-axis in the order A, B. C. At "' = 1 = 0, B sends pulses of light towards both A and C. (i) State Einstein's second postulate. (ii) Sketch space-time diagrams, cr'-vs-x' for frame S' and cr-vs-x for frame 5, show- ing A and C's worldlines and the events marking their reception of the light pulses from B. Hence demonstrate graphically that two events which are si- multaneous in one inertial frame are not necessarily simultaneous in a different inertial frame. b) Three inertial frames, S. S' and S", have axes and origins aligned in the standard fashion. Frames S' and 5" move at +0.8c and -0.8c respectively along the .x-axis relative to frame 5. An event takes place on the x, x' and ." axes. In frame S' the event is measured to be at /' = 2.0s, x' = 6.0 x 10 m. (i) Calculate the coordinates, / and x. of the event in S. (ii) Calculate the coordinates, " and x", of the event in $". (iii) Calculate the time in each of the three frames that light from the event will reach the respective spatial origin of that frame. (iv) Explain whether the arrival of the light from the event at the spatial origin of each frame marks a single event or three separate events. c) A particle of rest mass 0.9GeV/c' has kinetic energy 2GeV. Calculate the particle's (i) Lorentz factor. (ii) speed, as a fraction of the speed of light. (iii) momentum. (iv) rest mass in kilograms