Directional derivative in space?

[mrjust]

I saw a similar problem on here, but didn't quite understand it. I have tried to solve this using the method below using different approaches but I'm having trouble solving it. Can you tell me what I'm doing wrong? I'm about to give up on it.

I have tried the following,
first I found the partial derivative of P with respect to h

dp/dh = 30(-3.23*10^-5)e^(-3.23*10^-5h)

I set h=0 and this gave me :

grad P= 30(-3.23*10^-5)k

It is in the z direction because pressure only depends on height.
I should now find my directional derivative so this is what is got:

directional derivative = sqrt( {30(-3.23*10^-5)}^2)*cos(90+25)=-4.0952 (what are the units for this I'm unsure? Hg/ft?
I'm unsure of the value of theta. I think it should be that because grad P is pointing directly downward.

Now I converted my 120mph in to in/sec --> (120*5280*12)/3600 = 2112 in/sec

I think I'm getting lost at this step.

The quality of the picture is bad, here is a backup link..

http://bayimg.com/bAllPAaFH

 

[JSS]

I'm just another student here, so don't be expecting me to answer your problem, but I wonder if you wouldn't mind discussing it with me. Perhaps I'm confused, but it seems that you have the rate of change at 0 level in Hg/ft and only need to resolve how fast the plane is ascending in ft/s.

The vertical speed is simply 120*sin(25°) m/h which you have to convert to ft/s.
Then isn't it just a matter of RateOfChange (Hg/ft) * VerticleVelocity (ft/s)?. That would give you Hg/s, which seems what is being asked.

Or am I totally lost too?