Question

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Answer 1

An airplane is flying at a fixed altitude of \(one~mile\), at the constant rate of \(525 mi/hr \). A radar station on the ground is tracking the path of the airplane. At the instant when the airplane is \(two~miles\) past the point directly above the radar station, what is the rate at which the distance from the station to the plane is changing?

Answer 2

We need the distance first b4 we can do some awesome calculus.

Answer 3

at time t:
y: distance between station and plane
x: distance between station and horizontal projection of the plane

y2 = x2 + 1
y2 - x2 = 1

differentiate both sides with respect to t
2yy' - 2xx' = 0

"At the instant when the airplane is two miles past the point directly above the radar station"
x'=525mi/hr. constant
x = 2 miles
y = radical(5)

you can get y'

Answer 4

Thank you guys :)

Answer 5

any time :)