1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Directional derivatives

  1. Apr 15, 2012 #1
    1. The problem statement, all variables and given/known data
    A bush-walker is climbing a mountain, of which the equation is [itex]h \left( x,y \right) =400-{\frac {1}{10000}}\,{x}^{2}-{\frac {1}{2500}

    The x-axis points East, and the y-axis points North. The bush-walker is at a point P, 1600 metres West, and 400 metres South of the peak.

    What is the slope of the mountain at P in the direction of the peak?

    3. The attempt at a solution

    I'm fairly sure on how to solve this, except I need a few different elements. Since we have the starting point, I can calculate the gradient at that point. I need to find a directional vector (to the peak) from that point, and that's what I'm not sure to find.

    Looking at the equation for the mountain, I'm guessing its peak is when (x,y) = (0,0)

    I first tried for v = +1600i + 400j, but that was not correct.

    The answer 8/5*sqrt(17) = 0.388
    Last edited: Apr 15, 2012
  2. jcsd
  3. Apr 15, 2012 #2
    NVM, I figured it out. I was mistakenly keeping the 400 as part of the equation whilst calculating the gradient.
    Last edited: Apr 15, 2012
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook