Final answer:
The question deals with subtracting vectors graphically to determine the final position of a woman sailing a boat who has traveled incorrectly during one leg of her trip. It involves calculating vector components, combining them, and finding the differences to determine her unintentional endpoint compared to the intended dock.
Step-by-step explanation:
The question involves subtracting vectors graphically. We have a scenario where a woman is sailing a boat and needs to travel to a dock. She has to follow two directions: the first leg of the trip is 27.5 m at a 66.0° heading north of east, and the second leg is 30.0 m at a 112° heading north of east. If she incorrectly travels in the opposite direction for the second leg, we must determine her final position relative to the dock by subtracting the second vector from the sum of her position after the first leg and the second leg if it was in the correct direction.
To visualize and solve this, we can sketch the vectors on a coordinate system, add them to find the intended destination, and then subtract the second vector traveled in the wrong direction to find her erroneous position. This involves using trigonometric functions to decompose the vectors into their x and y components, adding or subtracting these components, and then finding the resultant vector's magnitude and direction to determine her final location relative to the dock.