A plane flying horizontally at an altitude of 2 mi and a speed of 420 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 5 mi away from the station.

Answer 1

well, after t hours, the plane has gone 420t miles.

So, the distance z is found using

z^2 = 2^2 + (420t)^2
so, that means that z is changing at

2z dz/dt = 2*420^2 t

now just plug in your numbers.