A postal employee drives a delivery truck over the route shown in Fig. E1.25. Use the method of components to determine the magnitude and direction of her resultant displacement. In a vector-addition diagram (roughly to scale), show that the resultant displacement found from your diagram is in qualitative agreement with the result you obtained by using the method of components.

Verified step by step guidance

1. Step 1: Break down the route into its vector components. The route consists of three segments: 2.6 km north, 4.0 km east, and 3.1 km at a 45° angle north-east.
2. Step 2: Convert the 3.1 km segment into its north and east components using trigonometry. For a 45° angle, both components are equal: 3.1 km * cos(45°) for the east component and 3.1 km * sin(45°) for the north component.
3. Step 3: Sum the north components: 2.6 km (north) + 3.1 km * sin(45°) (north-east component).
4. Step 4: Sum the east components: 4.0 km (east) + 3.1 km * cos(45°) (north-east component).
5. Step 5: Use the Pythagorean theorem to find the magnitude of the resultant displacement: sqrt((sum of north components)^2 + (sum of east components)^2). Determine the direction using the arctan function: arctan((sum of north components) / (sum of east components)).