Aspaceship travels at constant speed, vg = c away from earth. sixteen minutes after departure, according to the ship's clock, the pilot learns that a bomb has been placed on the ship. the bomb is programmed to explode 51 minutes after departure. (i) the pilot immediately escapes and returns to earth. the moment the escape pod leaves the ship the pilot sends a radio message to earth. show that the distance of the ship from earth in earth's reference frame, when the pilot escapes, is 30 light minutes (where 1 light minute is the distance travelled by light in 1 minute, 1 lmin = cx 1 min). calculate how many minutes after departure the message is received on earth. (ii) the escape pod blasts off from the ship with speed, v, = 24 c with respect to the ship and towards earth. unbeknown to the pilot, the bomb is actually in the escape pod. show that the speed of the escape pod with respect to earth is up= show that the distance of the escape pod from earth, in earth's reference frame, when the pod explodes, is light minutes. calculate how many minutes after departure earth sees the explosion. (iii) draw a spacetime diagram in earth's reference frame, depicting the world- lines of the ship, the escape pod, the pilot's signal and the light from the explosion. (iv) months later, the pilot's wrist-watch is recovered, which stopped at the moment of the explosion. the watch was set to 00: 00 at departure. state what was shown on the display.