A sailor in a small sailboat encounters shifting winds. She sails 2.00 km east, next 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. P1.64). 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 numerical solution.

Solution 72P Step 1: Let east be the positive x direction and north be the positive y direction. The first vector goes from point (0, 0) to point (2, 0). Southeast is 45 south of east. Step 2: East component = 3.5 cos 45 South component = -3.5 sin To determine the x component of this point, add 2 km. x = 2 + 3.5 cos 45 This is approximately 4.47 km. Second point = (2 + 3.5 cos 45, -3.5 sin 45) Step 3: The final point is (5.8, 0). To draw the third vector, draw a line from second point to the final point. To determine the x distance, subtract the x component of the second point from 5.8. x = 5.8 – (2 + 3.5 * cos 45)