1. Understand the Physics

* Projectile Motion: The golf ball's motion is a classic example of projectile motion. This means it's influenced by gravity, causing it to follow a parabolic path.

* Vertical Motion: The maximum height is determined by the vertical component of the initial velocity.

2. Break Down the Initial Velocity

* Vertical Component (v_y): v_y = v * sin(θ)

* v = initial speed (31 m/s)

* θ = launch angle (35°)

* v_y = 31 m/s * sin(35°) ≈ 17.75 m/s

3. Use the Kinematic Equation

* The relevant kinematic equation for vertical motion is:

* v_f² = v_i² + 2 * a * Δy

* Where:

* v_f = final vertical velocity (0 m/s at the maximum height)

* v_i = initial vertical velocity (17.75 m/s)

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

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

4. Solve for Maximum Height

* Substitute the known values into the equation and solve for Δy:

* 0² = (17.75 m/s)² + 2 * (-9.8 m/s²) * Δy

* 0 = 315.06 m²/s² - 19.6 m/s² * Δy

* 19.6 m/s² * Δy = 315.06 m²/s²

* Δy = 315.06 m²/s² / 19.6 m/s²

* Δy ≈ 16.07 meters

Therefore, the maximum height attained by the golf ball is approximately 16.07 meters.