Flight Paths An air traffic controller spots two planes at the same altitude flying toward each other (see figure). Their flight paths are 20° and 315°. One plane is 150 miles from point P with a speed of 375 miles per hour. The other is 190 miles from point P with a speed of 450 miles per hour.
(a) Find parametric equations for the path of each plane where t is the time in hours, with corresponding to the time at which the air traffic controller spots the planes.
(b) Use the result of part (a) to write the distance between the planes as a function of t.
(c) Use a graphing utility to graph the function in part (b). When will the distance between the planes be minimum? If the planes must keep a separation of at least 3 miles, is the requirement met?
