Understanding the Concepts

* Free Fall: An object in free fall is only under the influence of gravity. We assume no air resistance.

* Constant Acceleration: The acceleration due to gravity (g) is approximately 9.8 m/s². This means the object's speed increases by 9.8 m/s every second it falls.

* Kinematic Equations: We'll use a kinematic equation to relate the initial velocity, final velocity, acceleration, and distance traveled.

The Equation

The appropriate kinematic equation is:

v² = u² + 2as

where:

* v = final velocity (13 m/s)

* u = initial velocity (0 m/s since it starts from rest)

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

* s = distance fallen (what we want to find)

Solving for Distance (s)

1. Substitute the values:

13² = 0² + 2 * 9.8 * s

2. Simplify:

169 = 19.6s

3. Solve for s:

s = 169 / 19.6 ≈ 8.62 meters

Answer:

The freely falling object will have fallen approximately 8.62 meters when its instantaneous speed is 13 meters per second.