# an airplane flying at an altitude of 6 miles passes directly over a radar antenna. when the airplane is 10 miles away, the radar detects that the distance s is changing at a rate of 240 miles per...

an airplane flying at an altitude of 6 miles passes directly over a radar antenna. when the airplane is 10 miles away, the radar detects that the distance s is changing at a rate of 240 miles per hour. What is the speed of the airplane?

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The airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane is 10 miles away, the radar detects that the distance s is changing at a rate of 240 miles per hour.

If the distance of the aircraft from the radar is s, the height of the aircraft is H and B is the horizontal distance of the aircraft from the radar, `s^2 = H^2 + B^2` .

It is given that H = 6

=> B^2 = s^2 - 36

Take the derivative with respect to time of both the sides

`2*B*((dB)/(dt)) = 2*s*((ds)/(dT))`

If the distance is changing at the rate of 240 miles per hour when the aircraft is 10 miles from the radar, `(ds)/(dT) = 240` and s = 10, B = `sqrt(100 - 36)` = 8

`(dB)/(dt) = (10*240)/8` = 300 miles per hour

The speed of the aircraft is 300 miles per hour.

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