Question

6. (The Hill) Suppose you are standing on a hill. You have a topographic map, which uses rectangular coordinates (x,y) says your present location is at one of the following points (pick one): measured in miles. Your global positioning system А: (1,4), В: (4, -9), С:(-4,9), D:(1,—4), E: (2,0), F:(0,3) The height h of the hill in feet above sea level is given by 5000 ar2 by2 h(, y) 11 10ft 30 and b where a = mi2 mi2 (a) Starting at your present location, in what compass direction (2-d unit vector) do you need to go in order to climb the hill as Draw this vector on your topographic map steeply possible? as (b) How steep 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 (c) 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 y 0 5 -10 -6 -4 -29 2 4 6

Answer 1

Amswer aoba h= 5DOD-a-bzj the aooe fosmzla o,0) t E herghest outraft) he hillnd Rem an cation moio toond o) depest pals DEstmce te heght froheut to From potnt slepe (ttmi) clamb ACL-4) l8 37 10ft 4 12 mi 46 12 B4,-) 9.85 m8 1910 ft 130.76 q-85 mi 39104t 1290 ft 13096 DO-4 F(2,0) 49104t 4-12-mi 110ft 46 12 4940 fH 6oft 30 FO,3) 3 m3 4111 ff From he hble t to nasds 0en 15 cler ba stsh 29 kom or c fc lbe cteapest pal The vester fiom 41j 41- heigut to chnb om eihe bont h= 130.96f 3-D vector rom 8-41 +ni+ 130 «76 G he Vettoe rom C = 3-D vetor-feom 41-93t 130 6