Understanding the Physics

* Free Fall: The stone is in free fall, meaning the only force acting on it is gravity.

* Acceleration due to Gravity (g): We'll use the standard acceleration due to gravity, g = 9.8 m/s². This means the stone's velocity increases by 9.8 m/s every second.

* Initial Velocity (v₀): The stone starts with an initial velocity of 3 m/s.

* Displacement (Δy): The stone falls 93 meters (Δy = -93 m, negative since it's downward).

Formulas

We can use the following kinematic equations:

1. Displacement: Δy = v₀t + (1/2)gt²

2. Final Velocity: v = v₀ + gt

Calculations

1. Time (t):

* Substitute the known values into the displacement equation:

-93 m = (3 m/s)t + (1/2)(9.8 m/s²)t²

* Rearrange the equation into a quadratic equation:

4.9t² + 3t + 93 = 0

* Solve for 't' using the quadratic formula:

t = [-b ± √(b² - 4ac)] / 2a

where a = 4.9, b = 3, and c = 93

* Calculate the two possible values of 't'. The positive value will be the correct answer.

2. Final Velocity (v):

* Once you've found the time (t), plug it into the final velocity equation:

v = 3 m/s + (9.8 m/s²)t

Important Note: You'll likely get two solutions for 't' from the quadratic equation. Choose the positive solution, as time cannot be negative.

Let me know if you'd like to see the full calculation of the quadratic formula!