# Thread: Related Rates Problem

1. ## Related Rates Problem

Hey I've got a problem here involving related rates and i'm not too sure where to go with it.

An airplane is flying due east at 400 mph and passes over an airport 12 minutes before a second airplane flying south 30 degrees west at 500mph. If the planes are at the same altitude, how fast will they be seperating when the second plane is over the airport?
I tried drawing a diagram, but i'm not sure what it will look like, because when the second plane is over the airport, they are on the same path.

I tried finding the distance between the first airplane and the airport after 12 minutes, and then adding an additional amount of time to make a triangle, but we have too little information to use either sine or cosine law.

No idea where to go with this, any help appreciated!

2. Originally Posted by superduper
Hey I've got a problem here involving related rates and i'm not too sure where to go with it.

I tried drawing a diagram, but i'm not sure what it will look like, because when the second plane is over the airport, they are on the same path.

I tried finding the distance between the first airplane and the airport after 12 minutes, and then adding an additional amount of time to make a triangle, but we have too little information to use either sine or cosine law.

No idea where to go with this, any help appreciated!
1. Define a coordinate system: the x-axis pointing East and the y-axis pointing North.

2. Define the time "zero" when the second airplane is exactly over the airport. Then the first airplane has the position $a_1(80,0)$

3. In general: The positions of the airplanes can be calculated by:

$\begin{array}{l}a_1(400t+80,0) \\ a_2(-250t, -250\sqrt{3} t)\end{array} \ ,\ t\ measured\ in\ hours$

4. Now use the distance formula with these two positions.

5. I'll leave the rest for you.