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?
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.