Two rockets in interstellar space, initially separated by a distance of two light years, move toward each other with velocities 0.9c and -0.9c. a) What are the magnitudes of the velocities of each rocket in the other rockets inertial frame? b) For an observer on either of the rockets now much time has elapsed when it reaches the other rocket? c) When the rockets meet, what contracted distance to they calculate that they have traveled? d) Using a Lorentz transformation (or two transformations, both work) numerically show that the same amount of time has elapsed on the clock of the second rocket ship by comparing the difference between initial and final times for a clock on the second rocket ship as calculated, via Lorentz transformation(s), from initial and final times on the first rocket ship. Hint: The observers on the rocket ships might not agree on simultaneity of the start of end of events so you can compare a time interval between the initial and final times instead to avoid that problem.