EXERCISES

1. At 7:41 PM, a UPS 747 cargo plane flying over central Maryland has just been vectored straight to the UPS hub in Louisville. At the same moment, a United 767 carrying 109 passengers is flying over northern Virginia on its way to Denver. It is also flying in a straight line. The Louisville-bound plane is flying at a constant speed of 480mph, while the Denver-bound plane is flying at a 505mph. Since both planes are basically flying west, both have been assigned an altitude of 27,000 ft. You are sitting in East-Central Air Traffic Control in Indianapolis, and you are concerned that these planes may come within 10 miles of each other, violating an FAA regulation. How close will the planes actually come; does one or the other need to be assigned to another altitude? What is the minimum distance between the two, and when and where does it occur? Please explain how you found your answer. For convenience, suppose Louisville is at the origin (0,0), Denver is at (-1120,10), the UPS flight is at (405,90), and the United flight is at (430,5) (all positions in miles).