Luke Skywalker ( m = 100 kg) fell from rest off of antenna below Cloud City of Bespin (height = 100000 m). Suppose that he missed Millennium Falcon waiting below and continued to plummet. Assume gravitation constant of Bespin is 10 m/sec 2, and Force provides resistance proportional to magnitude of the velocity, with a drag coefficient of k = 4.
i) Determine Luke's velocity v(t) and displacement X(t).
ii) Determine Luke's limiting velocity.
iii) Assume it would take 200 seconds for Millennium Falcon to shake off pursuing TIE fighters and to turn around for the second rescue attempt. How far from ground would rescue be made?