Chapter 4
Differential Calculus and Its Uses
Project 1: Air Traffic Control
Northwest Flight 1484 (an Airbus 320) is traveling from Minneapolis to New Orleans, and American Flight 2 (a Boeing 767) is traveling from Los Angeles to New York. (Map) Both flights are at 33,000 feet, and the flight paths intersect over Granger, Missouri. At 2:45 P.M. (Central time), the Northwest flight is 32 nautical miles (horizontally) from Granger and is approaching the intersection point on a course (or heading) of 171 degrees at a rate of 405 knots (nautical miles per hour). The American flight is 44 nautical miles from the intersection point and is approaching it on a course of 81 degrees at a rate of 465 knots.
- At this instant, how fast is the distance between the planes decreasing?
- How close will the planes come to each other? Will they violate the FAA's minimum separation requirement of 5 nautical miles? Will they collide if Air Traffic Control does not take action to separate them?
- What time will it be at the time of closest approach? Is there enough time for ATC to take appropriate action?
Click on the image at left to see a simulation of a day in the life of Air Traffic Control (13 MB QuickTime movie).