Homework SourseA plane flying due east at an altitude of 2 miles and a spee
A plane flying due east at an altitude of 2 miles and a speed of 490mi/h passes directly over a radar station. Find the rate at which the angle of elevation between the plane and the radar station is changing when the plane is 10 miles away from the station.
Solution
x^2 + y^2 = z^2 2x * dx/dt + 2y * dy/dt = 2z * dz/dt x * dx/dt + y * dy/dt = z * dz/dt x = 10 y = 2 dx/dt = 490 z = sqrt(104) dy/dt = 0 10* 490 = sqrt(104)* dz/dt 480.5 = dz/dt The distance is increasing at 480.5 mi/h
