The problem below refers to a vector $V$ with a magnitude $|V|$ that forms an angle $\theta$ with the positive $x$-axis. In each case, give the magnitudes of the horizontal and vertical vector components of $V$, namely $V_{x}$ and $V_{y}$ respectively. Round answers to the nearest tenth.
\[
\begin{array}{l}
|V|=14.6, \theta=48.9^{\circ} \\
V_{y}= \\
V_{x}=
\end{array}
\]

Step 1 ：Given the magnitude of vector $V$ as $|V|=14.6$ and the angle it forms with the positive $x$-axis as $\theta=48.9^\circ$.

Step 2 ：The magnitude of the horizontal component $V_{x}$ is given by $|V| \cdot \cos(\theta)$ and the magnitude of the vertical component $V_{y}$ is given by $|V| \cdot \sin(\theta)$.

Step 3 ：Converting the angle to radians, we get $\theta_{rad} = 0.8534660042252271$.

Step 4 ：Substituting the values into the equations, we get $V_{x} = 9.6$ and $V_{y} = 11.0$.

Step 5 ：Final Answer: The magnitudes of the horizontal and vertical vector components of $V$ are $V_{x} = \boxed{9.6}$ and $V_{y} = \boxed{11.0}$ respectively.