A canoe has a velocity of 0.300 m / s southeast relative to the earth. The canoe

Question

A canoe has a velocity of 0.300m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.600m/s east relative to the earth. (Figure 1)

Find the direction of the velocity of the canoe relative to the river.

**The answer I came up with was:

You may need to review Calculating Trigonometric Function Values.

I don't understand how this is wrong?

61.32 degrees south of west A canoe has a velocity of 0.300m/s southeast relative to the earth. The canoe is on a river that is flowing at 0.600m/s east relative to the earth. (Figure 1) Find the direction of the velocity of the canoe relative to the river.

Explanation / Answer

Let the canoe's velocity equal a, the river's velocity equal b, and the resultant's velocity equal c.

In vector problems, use the tail-to-tip method when graphing. Draw an arrow headed east for the 0.6 m/s and, off of the tip, draw an arrow headed southeast for 0.3 m/s. Draw the resultant.

The angle in between a and b is 135 degrees, because the perpendicular (90) plus the 45 degrees determines that.
Now, use the law of cosines to determine the magnitude.

c^2 = a^2 + b^2 - 2(a)(b)cos(c)

c^2 = 0.09 + 0.36 + 0.2545

c = 0.839 m/s

Now, to determine direction, use the law of sines.

a / sina = b / sinb = c / sinc

0.839 / sin135 = 0.3 / sinx

x = 14.65 degrees.

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