Question

Suppose you are standing on a hill. You have a topographic map, which uses rectangular coordinates (ry) measured in miles. Your global positioning system says your present location is at one of the following points (pick one): A: (1.4) B: (4.-9) C: (-4,9) D: (1.-4) E: (2.0) F: (0,3) Your guidebook tells you that the height h of the hill in feet above sea level is given by 11 = 5000 - ar? - by2 where a = 30 ft and 6 = 10 ft 10 1. Starting at your present location, in what compass direc- tion (2-d unit vector) do you need to go in order to climb the hill as steeply as possible? Draw this vector on your topographic map. 2. How stoep is the hill if you start at your present location and go in this compass direction? Draw a picture which shows the slope of the hill at your present location. 3. In what direction in space (3-d vector) would you actually be moving if you started at your present location and walked in the compass direction you found in the previous problem? To simplify the computation, your answer does not need to be a unit vector -10 6