A controller spots two planes at the same altitude flying toward each other (see figure). Their
flight paths are
. 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
is the time in hours, with
corresponding to the time at which the air traffic controller spots the planes.
b) Use the result in part (a) to write the distance between the planes as a function of
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?
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