Calculating speed of an airplane

Question

An airplane is flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane is 10 miles away (s=10), the radar detects that the distance s is changing at a rate of 260 miles per hour. What is the speed of the airplane?

Some help would be greatly appreciated.

Answer 1

There are 2 possible interpretations here and they effect the way the problem is solved.

If the distance s is measured horizontally from the radar detector, then the solution will be different from what I write below.

Draw a figure which will look like a right triangle with vertical leg 6, horizontal leg x and hypotenuse s.

x² = s² - 36

2x (dx/dt) = 2s (ds/dt)

Now plug in the values given (you will need to use both equations!) and solve for dx/dt.