Question

Two spaceships leave the Earth at time t-0 in opposite directions with velocities v, and v2 (v1 > v2). At a subsequent time ts, two light signals are sent from the Earth to both of the spaceships. E and E2 are the events of the light signal reached at spaceship 1 and spaceship 2 respectively. (a) Find ti and x of E, and the spatial coordinates of E, and Ea as viewed from (30 marks) the Earth. (b) Obtain the ratio between vi and v2 in order that the reception of the signals (30 marks) can be simultaneous in the reference frame fixed to the faster spaceship. (c) Draw the spacetime diagram of E1 and E2 in the reference frame of the Earth (40 marks) and spaceship 1. Mark all the relevant events and the worldlines.

Answer 1

Delta lambda = lambda^2/2 n gl cos theta rightwardsdoublearrow l = lambda^2/2 ng Delta lambda Given lambda = 6563: n = 5 R = squareroot 0.95 Therefore l = (6562)^2/2 times squareroot 0.95 times 0.136 = 0.016 m l = 1.6 cm \r\n Delta lambda = lambda^2/2 n f l cos theta rightwardsdoublearrow l = lambda^2/2 n g Delta lambda Given lambda = 6563: n = 5R = squareroot 0.95 Therefore l = (6563)^2/2 times squareroot 0.95 times 0.136 = 0.016 m l = 1.6 cm