Final answer:
The x-component of the vector d = (3.0 km, 30° left of +y-axis) is approximately -2.60 km, and the y-component is 1.50 km, calculated using the cosine and sine of 150°, respectively.
Step-by-step explanation:
To find the x- and y-components of the vector d= (3.0 km, 30° left of +y-axis), we first need to understand that the angle provided is measured counter-clockwise from the positive y-axis. The vector is pointing to the left (westward when considering the standard geographical orientation), thus forming an angle with respect to the negative x-axis. Using trigonometry, we can resolve the vector into its components.
The x-component (Dx) is found by multiplying the magnitude of the vector by the cosine of the angle, while the y-component (Dy) uses the sine of the angle:
- Dx = 3.0 km × cos(150°)
- Dy = 3.0 km × sin(150°)
Calculating these using the respective trigonometric functions, we get:
- Dx ≈ -2.60 km (rounded to two significant figures)
- Dy ≈ 1.50 km (rounded to two significant figures)
Therefore, the x- and y-components of the vector d are approximately -2.60 km and 1.50 km, respectively.