Understanding the Concepts

* Projectile Motion: The football's motion is a classic example of projectile motion. This means it's affected by gravity and follows a parabolic path.

* Vertical Velocity: The initial vertical velocity determines how high the football will go.

* Acceleration Due to Gravity: The only force acting on the football in the vertical direction is gravity (approximately -9.8 m/s²).

Steps to Solve

1. Find the Vertical Component of Initial Velocity:

* v₀y = v₀ * sin(θ)

* v₀y = 28.0 m/s * sin(60°)

* v₀y ≈ 24.25 m/s

2. Use the Vertical Kinematic Equation:

* v² = v₀² + 2 * a * Δy

* At the highest point, the vertical velocity (v) is 0 m/s.

* We know:

* v₀y = 24.25 m/s

* a = -9.8 m/s² (acceleration due to gravity)

* Δy = the maximum height (what we want to find)

3. Solve for Δy:

* 0² = (24.25 m/s)² + 2 * (-9.8 m/s²) * Δy

* 0 = 588.06 m²/s² - 19.6 m/s² * Δy

* 19.6 m/s² * Δy = 588.06 m²/s²

* Δy = 588.06 m²/s² / 19.6 m/s²

* Δy ≈ 30 m

Answer

The highest elevation reached by the football is approximately 30 meters.