Understanding the Concepts
* Free Fall: An object in free fall experiences only the force of gravity. We assume no air resistance in this problem.
* Initial Velocity: The object starts from rest, so its initial velocity (v₀) is 0 m/s.
* Final Velocity: The object's final velocity (v) is given as 10 m/s.
* Acceleration due to Gravity: The acceleration due to gravity (g) is approximately 9.8 m/s².
Using the Equation of Motion
We'll use the following equation of motion:
v² = v₀² + 2as
where:
* v = final velocity (10 m/s)
* v₀ = initial velocity (0 m/s)
* a = acceleration due to gravity (9.8 m/s²)
* s = distance fallen (what we want to find)
Solving for Distance (s)
1. Plug in the values:
10² = 0² + 2 * 9.8 * s
2. Simplify:
100 = 19.6 * s
3. Solve for s:
s = 100 / 19.6 ≈ 5.1 meters
Answer:
A freely falling object will have fallen approximately 5.1 meters from rest when its instantaneous speed is 10 meters per second.
