Help me with this quick please

Question

A airplane is 528 feet directly above an automobile and starts east at a rate of 20 miles an hour at the same instant the automobile starts east at the rate of 40 miles an hour. how fast are they separating

Answer 1

Let x: horizontal distance between the two. Let D: distance between the two

D² = x² + 528² ; x = 0 , D = 528 , dx/dt = 20 mph (the difference of their speeds)

2D·dD/dt = 2x·dx/dt

dD/dt = 0

At the initial instant, the distance between them is not changing. This is the same result as it would be if the car didn't start directly under the the plane, but instead caught up to and passed the plane (horizontally). In that situation, the distance between them would be decreasing until the instant the car was directly underneath the plane. At that instant, the distance between them would be at a local minimum (of 528 ft), the tangent line would be horizontal, and the distance between them would not be changing. It would be done decreasing and it would about to be increasing, and we would have a critical point for the distance graph.