Final answer:
The magnitude of a vector whose x-component is 2 units and whose angle is 60 degrees is 4 units. This is calculated by using the formula for the x-component of a vector and rearranging it to solve for the magnitude. Then, you plug in the given values for the x-component and the angle.
Step-by-step explanation:
The calculation for the magnitude of a vector includes understanding of its components and the angle it makes with the axes. Here, we have a vector with an x-component of 2 units and an angle of 60 degrees from the x-axis. The components of a vector V are Vx = V cos θ and Vy = V sin θ. However, in this case, we are given the x-component and angle with the x-axis and will work with Vx = V cos θ, where V is the magnitude we're looking for. Rearranging the equation we get V = Vx / cos θ.
Substituting the given values, we get V = 2 / cos(60°) = 2 / (1/2) = 4 units. Thus, the magnitude of the vector is 4 units, corresponding to Option 4 in your question. Always remember the trigonometric identities when dealing with vectors, as cosine equates to the adjacent side (x-component in this case) divided by the hypotenuse (which is the magnitude of our vector).
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