At a given moment, a plane passes directly above a radar station at an altitude of 6 km. The plane's speed is 800 km/h. Let ℎ be the distance between the plane and the station through the air.

Question

(a) How fast is the distance between the plane and the station changing half an hour later?

(Use decimal notation. Give your answer to three decimal places.)

𝑑ℎ𝑑𝑡≈

(b) How fast is the distance between the plane and the station changing when the plane passes directly above the station?

(Use decimal notation. Give your answer to three decimal places.)

𝑑ℎ𝑑𝑡≈

Answer 1

If the plane is x km from the point overhead, then
h^2 = 6 + x^2
h dh/dt = x dx/dt

Now you can answer the questions