On a training flight, a student pilot flies from Lincoln, Nebraska, to Clarinda, Iowa, next to St. Joseph, Missouri, and then to Manhattan, Kansas (Fig. P1.66). The directions are shown relative to north: 0o is north, 90o is east, 180o is south, and 270o 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.

Solution to 74P Here we need to find the distance to be travelled from Manhattan to Lincon and the direction to be taken. Step 1 Resolve all the components with respect to North direction. We need to consider the direction in cartesian coordinates. Thus North becomes y axis and East becomes x axis. Resolving the vector to North and East directions (a)Lincoln to Clarinda North:147cos85=12.811 km East:147sin85 = 146.44 km (b)Clarinda to St. Joseph Here the angle between East and the displacement vector is computed as (180-167=13, 90-13=77 degrees) North: 106sin77=103.283km East : 106cos77=23.844 km (c)St Joseph to Manhattan North:166sin35=95.2136 km East :166cos35=135.979 km