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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}
    }\,{y}^{2}
    [/itex]

    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
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