please explain ! (15 points) Suppose you are climing a hill whose shape is given
ID: 2841194 • Letter: P
Question
please explain !
(15 points) Suppose you are climing a hill whose shape is given by the equation z = 1000 - 0.0lx2 -0.02y2, where x, y and z are measured in meters. Here, x and y are horizontal coordinates while z denotes elevation above sea level. Assume that the earth is flat and the vector i points to the north and j points to the east. Suppose you start off from the point whose x and y coordinates are (50, 80). If you walk due south, will you ascend, or will you descend? At what slope? In what direction should you start out in order to go downhill as steeply as possible? If you walk northwest at a rate of 2 meters per second, how fast would you be ascending/descending?Explanation / Answer
z = 1000-0.01x^2 -0.02y^2
If x is positive you are moving north otherwiswe south
Similarly if y is positive youare moving east otherwise west
Given x (50,80)
z = 1000-0.01*50^2 -0.02*80^2 = 847
z = 1000-0.01x^2-0.02*80^2 = 872-0.01x^2
dz/dx = -0.02x
Your were walking south so x<0 So dz/dx = -0.02*50 = -1
Slope = -1 and you will descend
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