Understanding the Concepts
* Free Fall: The ball is in free fall, meaning the only force acting on it is gravity.
* Acceleration due to Gravity (g): This is the constant rate at which objects accelerate downwards due to gravity, approximately 9.8 m/s².
* Initial Velocity (v₀): Since the ball is dropped, its initial velocity is 0 m/s.
* Final Velocity (v): This is the velocity we want to find.
* Distance (d): This is the height from which the ball is dropped, 16 meters.
Using the Equations of Motion
We can use the following equation of motion to find the final velocity (v):
v² = v₀² + 2 * a * d
Where:
* v = final velocity
* v₀ = initial velocity (0 m/s in this case)
* a = acceleration due to gravity (9.8 m/s²)
* d = distance (16 m)
Calculations
1. Plug in the values:
v² = 0² + 2 * 9.8 m/s² * 16 m
2. Simplify:
v² = 313.6 m²/s²
3. Solve for v (take the square root):
v = √313.6 m²/s² ≈ 17.7 m/s
Answer: The ball will be traveling at approximately 17.7 m/s when it hits the ground.
