An aero plane is 528 ft. directly above an automobile and starts at the rate of 20 miles per hour at the same instant the automobile starts east at the rate of 40 miles an hour.

Question

How fast are they separating? 

Answer 1

Imagine a moment when the airplane is behind the car and a triangle formed by line from the airplane to the car some distance behind the car, the horizontal separation (S) and the height (h). The distance (D) between the plane and the car then becomes D² = 528²+S² where S= (40-20)t. To find dD/dt (which is the rate of separation), take the derivative finding dD/dt=400t/D. Note that at t=0, D=528 and dD/dt=0 !