\bullet On a training flight, a student pilot flies from Lincoln, Nebraska to Clarinda, Iowa, then to St. Joseph, Missouri, and then to Manhattan, Kansas (Fig. 1.30). The directions are shown relative to

north: $0^{\circ}$ is north, $90^{\circ}$ is east, $180^{\circ}$ is south, and $270^{\circ}$ is west. Use the method of components to find (a) the distance she has to fly from Manhattan to get back to Lincoln, and (b) the direction (relative to north) she must fly to get there. Illustrate your solutions with a vector diagram.