Final answer:
The total displacement of the speed boat is 287.5 m east, 124.3 m north.
Step-by-step explanation:
To find the total displacement of the speed boat, we can add up the individual displacements along with their respective directions. We can break down each displacement into its horizontal and vertical components and then add them up separately. Let's start by the first displacement of 650 m 45° north of west.
The horizontal component of this displacement is 650 m * cos(45°) = 460.5 m west, and the vertical component is 650 m * sin(45°) = 460.5 m north.
The second displacement of 400 m 10° north of east can be broken down into a horizontal component of 400 m * cos(10°) = 394.1 m east, and a vertical component of 400 m * sin(10°) = 69.3 m north.
The third displacement of 550 m, 130° can be broken down into a horizontal component of 550 m * cos(130°) = -227.7 m east, and a vertical component of 550 m * sin(130°) = 510.7 m south.
The final displacement of 350 m, 168° can be broken down into a horizontal component of 350 m * cos(168°) = -339.4 m east, and a vertical component of 350 m * sin(168°) = 105.2 m south.
By adding up the horizontal and vertical components separately, we get a total horizontal displacement of -339.4 m + 394.1 m - 227.7 m + 460.5 m = 287.5 m east, and a total vertical displacement of 105.2 m + 69.3 m - 510.7 m + 460.5 m = 124.3 m north.
Therefore, the total displacement of the speed boat is 287.5 m east, 124.3 m north.