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Question

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 150 miles from the point and has a speed of 900 miles per hour. The other is 200 miles from the point and has a speed of 1200 miles per hour.

(a) At what rate is the distance between the planes changing?

(b) How much time does the controller have to get one of the airplanes on a different flight path?

Answer 1

D = √((900 - 150t)² + (1200 - 200t)²) =

|300 - 50t|√((3² + 4²) ) =

50 |6 - t| * 5 =

250|6 - t|

D' = -250 t < 6

250 t > 6

(except for the minor problem at t = 6, when D = 0, which makes the second statement irrelevant)

a) For t < 6, including t = 0, this case, D' = -250

They are moving together at 250 mph

b) They meet when D= 0

250|6 - t| = 0

|6 - t| = 0

t = 6