A plane flying horizontally at an altitude of 1 mi and a speed of 560 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

when the plane has traveled x miles, the distance d is found using

d^2 = 1 + x^2
2d dd/dt = 2x dx/dt

when d=2, we have x=√3

2(2) dd/dt = 2√3 (560)
dd/dt = 485 mph