## Fundamentals of Physics Extended (10th Edition)

$221^{\circ}$ which is south west
We have three vectors representing the three parts of the path: $\vec{a} = 3.1\,km\, \hat{i}$ $\vec{b} = -2.4\,km\, \hat{j}$ $\vec{c} = -5.2\,km\, \hat{i}$ Add these up to get the total displacement: $\vec{t} = -2.1\,km\,\hat{i} - 2.4\,km\,\hat{j}$ The angle of the displacement is: $tan^{-1}(\frac{-2.1\,km}{-2.4\,km}) = 41^{\circ}$ Because both the x and y components are negative, we must add $180^{\circ}$ to get the correct answer (remember $tan^{-1}$ is restricted to between $-90^{\circ}$ and $90^{\circ}$): $221^{\circ}$ $221^{\circ}$ is southwest.