Final answer:
Margaret's total displacement after walking 0.930 mi west, 0.500 mi north, and 0.240 mi east is approximately 0.852 miles. This is calculated by summing the displacements in the x and y directions separately and then applying the Pythagorean theorem to find the magnitude.
Step-by-step explanation:
The student is asking about calculating displacement, which is a vector quantity representing the shortest path between the starting point and the final position of an object. Margaret walks to the store using the following path: 0.930 mi west, then 0.500 mi north, and finally 0.240 mi east. To find the magnitude of her total displacement, we need to calculate the resultant of these vectors considering the west direction as the negative x-axis and the north direction as the positive y-axis.
To calculate the resultant displacement, we first find the sum of the displacements in the x-direction (west-east) and the y-direction (north-south). The displacement in the x-direction is:
- -0.930 mi (west) + 0.240 mi (east) = -0.690 mi
The displacement in the y-direction is:
To find the magnitude of her total displacement, we apply the Pythagorean theorem:
R = √((-0.690)^2 + (0.500)^2) = √(0.4761 + 0.25) = √(0.7261) = 0.852 mi
Therefore, the magnitude of Margaret's total displacement is approximately 0.852 miles.