You start at the origin and walk 3 m south, down the y-axis, then turn and walk

Question

You start at the origin and walk 3 m south, down the y-axis, then turn and walk southwest an additional 4 m at an angle of 210 degrees from the x-axis. Answer the following questions. It may help to make a sketch of tihs to complete problem.

Question (multiple choice). What is the angle of the displacement from the origin and the quadrant of the final position after both moves?

a)55.3 degrees and 1st quadrant
b)235.3 degrees and 3rd quadrant
c) 34.7 degrees and 3rd quadrant
d)-90 degrees on negative y-axis
e) 214.7 degrees in the 3rd quadrant

Explanation / Answer

It's B. You know third quadrant because it has to be between the angles.

And then it's about halfway between them since you walked about equal, a little less since 4 is bigger than 3, so closer to the 210. Which gets you 235.

You can also do the math. Divide into xs and ys then put back together.

So total in ys=-3+4sin(210 degrees)S

in the xs we get 4cos(210 degrees)W

then we do taninverse(y/x)

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