Final answer:
The x- and y-components of the vector (3.0 km, 24° left of +y-axis) are approximately -2.74 km and 1.22 km, respectively, calculated using trigonometric functions with the given magnitude and angle.
Step-by-step explanation:
To find the x- and y-components of the vector δ⟷ = (3.0 km, 24° left of +y-axis), we can use trigonometric functions. Since the angle is given as left of the +y-axis, this means the vector is primarily pointing upwards, with a slight shift to the left, which in Cartesian coordinates corresponds to a positive y-component and a negative x-component.
Let's denote the magnitude of the vector as D and the angle with respect to the +y-axis as θ. The x-component Dx can be found using the cosine function, while the y-component Dy can be found using the sine function, with both considering the given angle.
Dx = -D × cos(θ)
Dy = D × sin(θ)
Here, D is 3.0 km and θ is 24°.
Dx = -3.0 km × cos(24°)
Dy = 3.0 km × sin(24°)
Calculating the numerical values:
Dx ≈ -3.0 km × 0.9135 ≈ -2.74 km
Dy ≈ 3.0 km × 0.4067 ≈ 1.22 km
Thus, the x-component is approximately -2.74 km, and the y-component is approximately 1.22 km. The answer should be given as -2.74 km, 1.22 km.