To solve this problem, we need to calculate the initial horizontal velocity of the football.

Given:

• The angle of projection, $\theta = 37.0^\circ$
• The initial velocity of the football, $v = 25.0 \, \text{m/s}$

The initial horizontal velocity component, $v_x$, can be calculated using the formula: $v_x = v \cdot \cos(\theta)$

Calculation

1. Substitute $v = 25.0 \, \text{m/s}$ and $\theta = 37.0^\circ$ into the formula.
2. Use the cosine value for $37.0^\circ$, which is approximately $\cos(37.0^\circ) \approx 0.7986$.

$v_x = 25.0 \, \text{m/s} \times 0.7986$ $v_x \approx 19.965 \, \text{m/s}$

Answer

The initial horizontal velocity of the football is approximately: $v_x \approx 19.97 \, \text{m/s}$

Would you like further details or explanations?

Here are five related questions to expand your understanding:

1. How can you calculate the initial vertical velocity component of the football?
2. What is the significance of breaking down the velocity into horizontal and vertical components?
3. How would the initial horizontal velocity change if the angle were increased?
4. What factors affect the horizontal distance the football will travel?
5. How does the initial velocity affect the maximum height the football can reach?

Tip: Remember, for any projectile motion, the horizontal velocity remains constant throughout the flight (assuming no air resistance).