Final answer:
The question deals with finding the components of a vector with a given magnitude and direction. By adjusting the angle provided from the y-axis to the x-axis and using trigonometric functions, the horizontal and vertical components can be determined.
Step-by-step explanation:
The question involves a vector with a magnitude of 187 meters and a direction of 25.1 degrees measured counterclockwise from the positive y-axis. To find the x and y components of this displacement vector (δ), we need to use trigonometry, considering the angle provided and the fact that the magnitude of the unit vector is 1.
To compute the x and y components, we'd use the cosine and sine functions respectively. Since the angle is given from the positive y-axis, the usual convention of measuring from the positive x-axis is rotated by 90 degrees. This means that to find the correct components relative to the x and y-axes, we should adjust the angle by subtracting it from 90 degrees if using standard trigonometric functions. Therefore, δx = δ cos(90° - θ) and δy = δ sin(90° - θ).
This would result in the components δx = 187 cos(64.9°) and δy = 187 sin(64.9°), which reveals the horizontal and vertical components of the displacement vector in the Cartesian coordinate system.