A plane flying horizontally at an altitude of 2 miles and a speed of 550 mi/h passes directly over a radar station

Question

A plane flying horizontally at an altitude of 2 miles and a speed of 550 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 has a total distance of 5 miles away from the station. (Round your answer to the nearest whole number.)

Answer 1

d² = 2² + x²; 2ldl/dt = 2xdx/dt, or dl/dt = x/ldx/dt; dx/dt = 550 mi/h; x = (25 - 4)^1/2 = 21^1/2 = 4.5826 mi

dl/dt = 4.5826mi·550mi/h/5mi = 504.08 mi/h