Expert: Paul Klarreich - 3/27/2009

Question
An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other.  One plane is 150 miles from the point and is moving at 450 mph. The other plane is 200 miles from the point and has a speed of 600 miles per hour.
a) At what rate is the distance 's' between the planes decreasing?
b) How much time does the traffic controller have to get one of the planes on a different flight path?

Answer
Questioner:   Neka
Country:  Bahamas
Category:  Calculus
Private:  No
 
Subject:  related rates
Question:  An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to each other.  One plane is 150 miles from the point and is moving at 450 mph. The other plane is 200 miles from the point and has a speed of 600 miles per hour.
a) At what rate is the distance 's' between the planes decreasing?
b) How much time does the traffic controller have to get one of the planes on a different flight path?
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Let  x = distance from plane 1 to the point.
Let  y = distance from plane 2 to the point.
    r = distance between planes.

Rates

dx/dt = -450
dy/dt = -600
dr/dt to be found.

relation:

x^2 + y^2 = r^2

Diff:

2x dx/dt + 2y dy/dt = 2r dr/dt

x dx/dt + y dy/dt = r dr/dt

Values:

x = 450
y = 600

Compute r = 750.

Now substitute and solve for r.

part (b), I THINK you can figure that one.
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Related Rates

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