Question

A plane flying horizontally at an altitude of 1 mi and a speed of 580 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station. (Round your answer to the nearest whole number.)

Answer 1

First, you need an equation that relates all of the variables. It is the pythagorean theorem.

Implicitly differentiate both sides.

Divide by 2

Plug in known values. We know a,b,and c. da/dt is the derivative of a, but since a is a constant that doesnt change, da/dt=0. db/dt is the change in b with respect to time (same as the derivative). db/dt =480, which was given.

This is the rate at which the distance is inreasing.


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Answer 2

OK THANKS! =)

Answer 3

No Problem hope it helps

Answer 4

So its a (da/dt) + b(db/dt) = c (dc/dt). Then it becomes 1(0) + radical 3* 580 = dc/dt.
How come we dont use the value 2 in the equation? My final answer is 580*radical 3, which is about 1005. When i put it into my hw it marks it wrong. Did i do it correctly?

Answer 5

Your thinking is correct, you need to divide 2:
c' = 580 √ 3/ 2