As she picks up her riders, a bus driver traverses four successive displacements represented by the expression $\begin{array}{l}(-6.30\mathrm{b})\hat{\mathrm{i}}-\left(4.00\mathrm{b}\cos 40^{\circ }\right)\hat{\mathrm{i}}-\left(4.00\mathrm{b}\sin 40^{\circ }\right)\hat{\mathrm{j}}\\ +\left(3.00\mathrm{b}\cos 50^{\circ }\right)\hat{\mathrm{i}}-\left(3.00\mathrm{b}\sin 50^{\circ }\right)\hat{\mathrm{j}}-(5.00\mathrm{b})\hat{\mathrm{j}}\end{array}$ Here b represents one city block, a convenient unit of distance of uniform size; i is east; and $\hat{\mathbf{j}}$ is north. The displacements at $40^{\circ }$ and $50^{\circ }$ represent travel on roadways in the city that are at these angles to the main east-west and northsouth streets. (a) Draw a map of the successive displacements. (b) What total distance did she travel? (c) Compute the magnitude and direction of her total displacement. The logical structure of this problem and of several problems in later chapters was suggested by Alan Van Heuvelen and David Maloney, American Journal of Physics $67(3)252-256$ March 1999.

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