# Bob walked 7.00 meters West, turned 25.0 degrees toward South, and then continued 9.00 meters. What is the direction of his displacement?

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To find the direction of displacement, you start by plotting the steps Bob has walked. After going 7 meters west, he turned 25 degrees south, so you must put that angle in his path. Then, he continued 9 meters. His displacement is simply the difference between his initial position and his final position, so we can treat it as a single scalar, the green line.

Now, calculate the displacement in the x-axis and y-axis directions using cosine and sine. In this case, you get 3.80 meters in the negative y direction (from 3.8=9arccos(25)) and 15.15 meters in the negative x direction (from 7+9arcsin(25)).

Recall the tangent function, tan(theta)=y/x . We already have the x and y components, so we can reconstruct the scalar with theta=arctan(3.80/15.15). Theta is then simply 14 Deg.

This gives us the direction relative to the negative x axis, in the counterclockwise direction. There are then a few ways of writing the answer:

- 256 degrees
- 14 degrees south of west
- 194 degrees counterclockwise from the x axis

All of these are correct.