# Directional derivatives

1. Sep 29, 2009

### bodensee9

1. The problem statement, all variables and given/known data
Hello:
An airplane is flying near a radar tower. At the instant it is exactly 3 miles due west of the tower. It is 4 miles high and flying with a ground speed of 450 mph and climbing at rate of 5 mph. If at the instant it is flying east, what is the rate of approach to the tower.

So I think this means that its position is [-3 0 4] if we take the tower to be located at [0 0 0] and its velocity is [450 0 5]. I thought that the derivative of the position function evaluated at [-3 0 4] and multiplied by the velocity vector will give us the rate of approach. But would the position function be [450t 0 5t]? This looks wrong.

Thanks!

2. Sep 29, 2009

### Dick

If you put t=0 into the position function you should get [-3,0,4], right? Doesn't that make the position function s(t)=[-3,0,4]+t*[450,0,5]?

3. Sep 29, 2009

### bodensee9

Hello:

Yes, but for some reason, I'm supposed to find the rate of approach (the tower). And the answer is 266 mph. But I'm not sure how I'm supposed to get that answer from what I have?

Thanks.

Last edited: Sep 29, 2009
4. Sep 29, 2009

### Dick

You need to find d/dt(|s(t)|). What's |s(t)|?