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Gradient Partial Derivative Problem

  1. Mar 2, 2009 #1
    1. The problem statement, all variables and given/known data
    The elevation of a mountain above sea level at (x,y) is 3000e^[tex]\frac{-x^2-2y^2}{100}[/tex] meters. The positive x-axis points east and the positive y-axis points north. A climber is directly above (10,10). If the climber moves northwest, will she ascend or descend and at what slope.

    2. Relevant equations
    [tex]\frac{d}{dx}[/tex]eu=eu[tex]\frac{du}{dx}[/tex]

    3. The attempt at a solution
    [tex]\nabla[/tex]f(10,10)=-600e-3i-1200e-3j

    I know that the climber will descend but I don't know how to figure out the slope that she will descend at. Can anyone help?
     
  2. jcsd
  3. Mar 2, 2009 #2

    Dick

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    To find the slope you want to take the dot product of your gradient with a unit vector pointed in the northwest direction. Can you find one?
     
  4. Mar 2, 2009 #3
    Would the unit vector be 600e-3i-1200e-3j since west is the opposite of east?
     
  5. Mar 2, 2009 #4

    Dick

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    No. A UNIT vector pointing west would be -i. A unit vector pointing north would be j. Do you see why? Northwest is at a 45 degree angle to both of those. Finding a unit vector pointing NW has nothing to do with your gradient vector. It's a whole different problem.
     
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