Final answer:
To find the distance from the starting point, break down each displacement into its x and y components, add up the components separately, use the Pythagorean theorem to find the magnitude, and find the direction using inverse trigonometry.
Step-by-step explanation:
To find the distance from the starting point, we need to find the resultant vector of the two displacements. We'll break down each displacement into its x and y components using trigonometry. For the first displacement, 12.5 m at 20° west of north, the x-component is 12.5 * sin(20°) and the y-component is 12.5 * cos(20°). For the second displacement, 24 m at 40° south of west, the x-component is 24 * cos(40°) and the y-component is -24 * sin(40°) since it's south of west.
Next, we add up the x-components and the y-components separately to find the resultant x-component and the resultant y-component. Finally, we use the Pythagorean theorem to find the magnitude of the resultant vector, which gives us the distance from the starting point. The direction of the resultant vector can be found using inverse trigonometry.
Using the given values, we can calculate the distance from the starting point to be approximately 31.2 meters.