Understanding the Concepts

* Free Fall: An object in free fall experiences only the force of gravity. We assume no air resistance.

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

* Kinematic Equations: We can use the following kinematic equation to relate displacement, initial velocity, final velocity, and acceleration:

* v² = u² + 2as

where:

* v = final velocity (27 m/s)

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

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

* s = displacement (the distance we want to find)

Calculation

1. Plug the values into the equation:

27² = 0² + 2 * 9.8 * s

2. Simplify and solve for s:

729 = 19.6 * s

s = 729 / 19.6

s ≈ 37.2 m

Answer:

A freely falling object will have fallen approximately 37.2 meters when its instantaneous speed is 27 m/s.