Question

A disoriented physics professor drives 3.55 km north, then 2.75 km west, and then 1.40 km south. Find the direction of the resultant. (I got 141.98 as an answer, however, masteringphysics marked it as wrong)

Answer 1

From the plot we can see that

$$\tan \alpha=\frac{3.55-1.40}{2.75}=0.7818$$

So

$$\alpha=\tan^{-1}(0.7818)=38^{\circ}$$ $$\theta=180^{\circ}-\alpha=180^{\circ}-38^{\circ}=142^{\circ}$$

The direction of resultant is $38^{\circ}$ North of West.