A plane flying horizontally at an altitude of 1 mi and a speed of 510 mi/h passes directly over a radar station.

Question

Find the rate at which the distance from the plane to the station is increasing when it has a total distance of 2 mi away from the station. (Round your answer to the nearest whole number.)

Answer 1

D = √(x² + 1); dD/dt = xdx/dt/√(x² + 1); dx/dt = 510mi/h; 2 = √x² + 1; x² = 3, x = √3 = 1.732 mi

dD/dt = 1.732mi·510mi/h/2mi = 441.673 mi/h