1

So I'm doing Physics homework - and I already have a rather crappy understanding of vectors, this problem just frustrates me because I have literally 0 idea of what to do with the information it gives me. Could anyone break it down so that I can actually understand what it's saying?

Oasis B is a distance d = 9.0 km east of oasis A, along the x axis shown in the figure. A confused camel, intending to walk directly from A to B instead walks a distance W1 = 23 km west of due south by angle θ1 = 15.0°. It then walks a distance W2 = 30 km due north. If it is to then walk directly to B, (a) how far (in km) and (b) in what direction should it walk (relative to the positive direction of the x axis within the range (-180°, 180°])? Figure for problem

What does it mean by "due west of south?" Where does the 15 degree angle come in?

secondubly
  • 477
  • "west of due south by 15 degrees" = -90 - 15 = -105 degrees, as south is along the negative y axis, an angle of -90 degrees relative to the x axis – Simon S Jan 30 '15 at 02:43
  • Drop a point $W$ in Quadrant III. Then $\angle WAB$ is $105^\circ$ – turkeyhundt Jan 30 '15 at 02:50

2 Answers2

2

The blue arrow show the two stages of where the camel walked. The red arrow passes from where it wound up to Oasis B.

enter image description here

North is at the top of this graph. When the camel was facing South (toward the bottom of the graph), "West of South" would be 15º to the camel's right, since West is to the right when facing South (that is leftward from bottom on the graph $^*$). It then turned around and traveled North (back toward the top of the graph).

$^*$ The graph is an overhead view of these proceedings...

What the camel still needs to do is journey along the red vector. Part (a) asks how long this vector is and Part (b) asks what angle the vector makes above (positive) or below (negative) going straight to the right on the graph, that is, due East (the 0º reference direction).

colormegone
  • 10,842
1

Hint: You probably realize the camel's first segment puts him somewhere on a circle of radius $23$ around the origin. But in what direction? Well, you're told that it isn't due south, but rather rotated $15^{\circ}$ in a westerly way from due south. Since south is "down", west is "clockwise" along that circle from there. Can you get it from here?

MPW
  • 43,638