# Thread: Related Rates Word Problem

1. ## Related Rates Word Problem

An airplane 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 270 miles per hour. What is the speed of the airplane?

I've tried setting up this equation with A=pi r^2, pythagorean theorem, and other formulas.

I don't understand how to set it up, and how to solve it. I'm completely stumped. Please help!

2. Originally Posted by jjung411
An airplane 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 270 miles per hour. What is the speed of the airplane?

I've tried setting up this equation with A=pi r^2, pythagorean theorem, and other formulas.

I don't understand how to set it up, and how to solve it. I'm completely stumped. Please help!
Draw a picture. Draw a line from the radar to the airplane, a vertical line from the radar, and a horizontal line from the airplane. That gives you a right triangle so you can use the Pythagorean theorem. (I don't know why you would even consider " $\pi r^2$"- there are no circles here!)

One leg of the triangle is the vertical line which as a constant 6 mile length. The other leg is the horizontal line of flight of the airplane and you are not given its length (but can calculate at the given instant). The length of the hypotenuse is the distance to the airplane, 10 miles and is increasing at 270 mph. (I suspect that there is a picture in your textbook since you say " the airplane is 10 miles away (s = 10)" without telling us what "s" is!).

Set up the Pythagorean theorem from that and differentiate with respect to time. Solve for the rate at the length of the horizontal leg is changing.

Try that and if you have trouble, come back and show what you have done.