Understanding the Concepts

* Free Fall: When an object falls near the Earth's surface, it experiences constant acceleration due to gravity (approximately 9.8 m/s²).

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

d = v₀t + (1/2)at²

where:

* d = displacement (66 m)

* v₀ = initial velocity (0 m/s, since it's at rest)

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

* t = time (unknown)

Solving for Time

1. Rearrange the equation: Since we want to find the final velocity, we need to first find the time it takes for the rock to fall. We can rearrange the equation to solve for t:

t = √(2d/a)

2. Plug in the values:

t = √(2 * 66 m / 9.8 m/s²)

t ≈ 3.67 s

Finding the Final Velocity

Now that we know the time, we can use another kinematic equation to find the final velocity (v):

* v = v₀ + at

1. Plug in the values:

v = 0 m/s + (9.8 m/s²) * 3.67 s

v ≈ 36.0 m/s

Answer:

The speed of the rock after falling 66 meters is approximately 36.0 m/s.