An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 90 miles from the point and has a speed of 450 miles per hour. The other is 120 miles from the point and has a speed of 600 miles per hour. At what rate is the distance between the planes changing? Let 5 denote the distance in miles as shown in the following figure. The origin represents the point of convergence. 140 120 100 80 60 4O 20 K 20 4O 60 BO 1 DO The distance 5 between the planes is given by the formula, 5 = if x2 + ,2. Thus, 52 = X2 + yz. One plane is 90 miles away and moving towards the point of convergence at 450 miles per hour so X = 90 and dx__ E- :- The other plane is 120 miles away and moving towards the point of convergence at 600 miles per hour, so y = d 120 and = . d. |:| An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 90 miles from the point and has a speed of 450 miles per hour. The other is 120 miles from the point and has a speed of 600 miles per hour. Exercise (a) At what rate is the distance between the planes changing? Click here to beg Exercise (b) How much time does the controller have to get one of the airplanes on a different flight path? In part (a), it was found that the two planes were 150 miles apart and getting closer at the rate of 750 mph. Use the formula Time = w to nd the time that the air traffic controller has to get one of the planes on a pee different flight path. Time _ Distance _ Speed _ 750