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Question

Show that the sum of the vectors discussed in Example 3.2 gives the result shown in Figure 3.24.

Example 3.2: A woman sailing a boat at night is following directions to a dock. The instructions read to first sail 27.5 m in a direction $66.0^\circ$ north of east from her current location, and then travel 30.0 m in a direction $112^\circ$ north of east (or $22.0^\circ$ west of north). Find the location of the dock.

Question Image

$52.9 \textrm{ m, } 89.9^\circ \textrm{ N of W}$

Solution Video

# OpenStax College Physics Solution, Chapter 3, Problem 9 (Problems & Exercises) (5:48)

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4 votes with an average rating of 5.

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Submitted by featherbrain on Sat, 09/12/2020 - 04:59

If we were given this problem without the figure, how would we discern if the angle was 89.9 or 90.1? If I free-hand drew the graph, the angle would be so close to 90 I wouldn't know whether it was 0.1 to the west of 90 or 0.1 to the east of 90.

Submitted by ShaunDychko on Mon, 09/14/2020 - 10:43

With a free hand drawn figure it wouldn't be possible to have enough precision to claim 89.9 vs 90.1. I totally agree with your critique. The only reason we can claim precision to the tenths place is because we've done calculations, rather than drawn freehand. I've written 89.9 in the solution only because I chose to measure the angle clockwise starting from the negative x-axis, which is co-terminal with 90.1 degrees counterclockwise from the positive x-axis. Co-terminal is to say that the angle specifies exactly the same position, just with a different number/reference point.