Question

A plane flying horizontally at an altitude of 3 mi and a speed of 480 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 6 mi away from the station. (Round to the nearest whole number.)

Answer 1

Did you make a sketch and got a right-angled triangle?
let the horizontal distance between the plane and the station be x miles
let the distance between the plane and the station be y miles
given: dx/dt = 480 mph
find: dy/dt when y = 6

y^2 = x^2 + 3^2
when y = 6
36 = x^2 + 9
x = √27

2y dy/dt = 2x dx/dt
dy/dt = (x/y)dx/dt
= √27(480)/6
= 415.7 mph or 416 mph