An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane is 10 miles away (s = 10), the radar detects that the distance s is changing at a rate of 290 miles per hour. What is the speed of the airplane?

The speed of the airplane is 335 mile per hour.

From the diagram attached:

Using Pythagoras theorem:

S² = x² + 25   (1)

Differentiating both sides of the equation with respect to t:

The speed of the airplane is 335 mile per hour.

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Explanation:

Given

altitude of the Plane

When Airplane is away

Distance is changing at the rate of

From diagram we can write as

differentiate above equation w.r.t time

as altitude is not changing therefore

at

substitute the value we get

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that would be because of both gravity and friction. so     c