Understanding the Concepts

* Free Fall: The ball is subject to gravity, which causes a downward acceleration of approximately 9.8 m/s².

* Kinematic Equations: We can use the following kinematic equation to relate the initial velocity (v₀), final velocity (v), acceleration (a), displacement (Δy), and time (t):

v² = v₀² + 2aΔy

Solving the Problem

1. Define Variables:

* Δy = 12 m (positive since the ball is moving upward)

* a = -9.8 m/s² (negative since gravity acts downward)

* v = 0 m/s (the ball momentarily stops at its highest point)

* v₀ = ? (the initial velocity we need to find)

2. Apply the Equation:

0² = v₀² + 2(-9.8 m/s²)(12 m)

3. Solve for v₀:

0 = v₀² - 235.2

v₀² = 235.2

v₀ = √235.2 ≈ 15.34 m/s

Therefore, the ball must be thrown upward at approximately 15.34 m/s to reach a height of 12 meters.