Final answer:
The total displacement of the speed boat is -417.9 m east + 698.6 m north.
Step-by-step explanation:
To find the total displacement of the speed boat, we need to add up the individual displacements:
1. The initial displacement of 650 m at 45° north of west can be split into its x and y components. The x component is 650 * cos(45°) = 459.4 m west, and the y component is 650 * sin(45°) = 459.4 m north. Therefore, the initial displacement is 459.4 m west + 459.4 m north.
2. The second displacement of 400 m at 10° north of east can also be split into its x and y components. The x component is 400 * cos(10°) = 394.4 m east, and the y component is 400 * sin(10°) = 69.1 m north. Therefore, the second displacement is 394.4 m east + 69.1 m north.
3. The third displacement of 550 m at 130° can be split into its x and y components. The x component is 550 * cos(130°) = -514.5 m east, and the y component is 550 * sin(130°) = 254.5 m south. Therefore, the third displacement is -514.5 m east + 254.5 m south.
4. The final displacement of 350 m at 168° can be split into its x and y components. The x component is 350 * cos(168°) = -336.2 m east, and the y component is 350 * sin(168°) = -84.4 m south. Therefore, the final displacement is -336.2 m east + -84.4 m south.
To find the total displacement, we add up the x and y components:
Total x displacement = 459.4 m west + 394.4 m east + -514.5 m east + -336.2 m east = -417.9 m east
Total y displacement = 459.4 m north + 69.1 m north + 254.5 m south + -84.4 m south = 698.6 m north
The total displacement of the speed boat is therefore -417.9 m east + 698.6 m north.