Final answer:
The final displacement from the starting point is approximately 485.9 meters at 137.0° (south of west).
Step-by-step explanation:
To find the final displacement, we can break down each leg of the path into its x and y components. Starting with the 100.0 meters directly east, this can be broken down into 100.0 meters in the x-direction and 0 meters in the y-direction. Next, the 200.0 meters south can be broken down into 0 meters in the x-direction and -200.0 meters in the y-direction. Moving on to the 150.0 meters at an angle of 30.0° south of west, we can calculate the x and y components using trigonometry. The x component is 150.0 * cos(30.0°) = 150.0 * 0.866 = 129.9 meters and the y component is 150.0 * sin(30.0°) = 150.0 * 0.5 = 75.0 meters. Finally, for the 250.0 meters at an angle of 60.0° north of west, the x component is 250.0 * cos(60.0°) = 250.0 * 0.5 = 125.0 meters and the y component is -250.0 * sin(60.0°) = -250.0 * 0.866 = -216.5 meters.
To calculate the final displacement, we add up the x and y components. The x component is 100.0 + 0 + 129.9 + 125.0 = 354.9 meters. The y component is 0 - 200.0 + 75.0 - 216.5 = -341.5 meters. We can use the Pythagorean theorem to find the magnitude of the displacement: √(354.9^2 + (-341.5)^2) ≈ 485.9 meters. The direction can be found using trigonometry: arctan(-341.5 / 354.9) ≈ -43.0°. Since the displacement is in the fourth quadrant, we add 180° to get the final direction: -43.0° + 180° = 137.0°. Therefore, the final displacement from the starting point is approximately 485.9 meters at 137.0° (south of west).