74. A sailor in a small sailboat encounters shifting winds. She sails 2.00 km east, then 3.50 km southeast, and then an additional distance in an unknown direction. Her final position is 5.80 km directly east of the starting point (Fig. 1.39). Find the magnitude and direction of the third leg of the journey. Draw the vector addition diagram and show that it is in qualitative agreement with your On a training flight, a student pilot flies from Lincoln, Nebraska to Clarinda, lowa, then to St. Joseph, Missouri, and then to Manhattan, Kansas (Fig. 1.41) . The directions are shown relative to north: $0^{\circ}$ is north, 90° is east, 180° is south, and 270° 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. Mlustrate your solutions with a vector diagram.numerical solution.
