Answer to Question #93965 in Classical Mechanics for Shane

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.