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.

  1. At this instant, how fast is the distance between the planes decreasing?
  2. 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?
  3. 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).

Image credits

 

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