Final answer:
The angle a vector makes with the positive x-axis can be found using the cosine ratio; the angle is approximately 58.2 degrees for the vector with a magnitude of 25 m and an x-component of 12 m.
Step-by-step explanation:
To determine the angle a vector makes with the positive x-axis, we can use trigonometry since we have the magnitude of the vector and the length of the x-component. Specifically, the cosine of the angle (θ) that the vector makes with the x-axis is equal to the x-component divided by the magnitude of the vector.
Here is the formula:
cos(θ) = (x-component) / (magnitude)
By substituting the given values:
cos(θ) = 12 m / 25 m
Now calculate the angle:
θ = cos⁻¹(12/25)
θ = 58.2° (approx.)
Therefore, the vector makes an angle of approximately 58.2 degrees with the positive x-axis.