The problem asks to determine the horizontal component of vector $\vec{V}$ with a magnitude of $91.5 \, \text{m/s}$ and an angle of $78.7^\circ$ above the horizontal.

To calculate the horizontal component $V_x$, we use the cosine function: $V_x = V \cdot \cos(\theta)$ Where:

• $V = 91.5 \, \text{m/s}$ is the magnitude of the vector,
• $\theta = 78.7^\circ$ is the angle from the horizontal.

Let's calculate the horizontal component.The horizontal component of vector $\vec{V}$ is approximately $17.93$.

Do you want more details or have any questions?

Here are 5 related questions for practice:

1. How would you calculate the vertical component of vector $\vec{V}$?
2. What is the significance of the cosine function when determining vector components?
3. If the angle were larger than $90^\circ$, how would it affect the horizontal component?
4. How can the magnitude of a vector be found from its components?
5. What is the relationship between vectors and coordinate systems in physics?

Tip: When working with vectors, always make sure the angle is measured from the horizontal (or the axis in question) to apply trigonometric functions correctly.