A secret communist spacecraft is observed approaching earth at 0.500c along a straight line from mars to earth.
1.) What distance does the spacecraft observe between mars and earth if earth based measurements show a distance between those objects of 40.0 million miles?
2.) The spacecraft prepares its nuclear weapons during a 20.0 minute warm up time measured in their frame of reference. How long is earth's measurement of their warm up time?
3.) The spacecraft launches a missile towards earth at a velocity of 0.900c measured relative to their ship. What speed does an earth based measurement show for the approach of the missile?
This problem is a good example of application of relativistic length contraction, time dilation and velocity transformation.