A plane flying horizontally at an altitude of 5 mi and a speed of 600 mi/h passe

Question

A plane flying horizontally at an altitude of 5 mi and a speed of 600 mi/h passes directly over a radar station. Find the rate in mi/h at which the direct line distance from the plane to the radar station is increasing when it is 6.5 mi away from the station.

Let x = the horizontal distance from the plane to the radar station.
Let y = the direct line distance from the plane to the radar station.

e) Substitute the given information into this equation and find the unknown rate. Express your answer in the form dx/dt or dy/dt = a number.

Explanation / Answer

e) y = 6.5 mi

x = sqrt( (6.5)^2 - 5^2) = 4.1533 mi

dy/dt = (x/y) dx/dt = (4.1533/6.5) * 600 = 388.38 mi/h

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