To calculate the depth of the well, we can use the formula for distance under constant acceleration due to gravity:

$d = \frac{1}{2} g t^2$

Where:

• $d$ is the depth of the well (in meters),
• $g$ is the acceleration due to gravity ($9.8 \, \text{m/s}^2$),
• $t$ is the time it takes for the stone to hit the water (in seconds).

Given $t = 9.5 \, \text{seconds}$, let's calculate the depth:

$d = \frac{1}{2} \times 9.8 \times (9.5)^2$

Now, calculating this:

$d = 0.5 \times 9.8 \times 90.25 = 441.225 \, \text{meters}$

So, the depth of the well is approximately 441.23 meters.

Would you like more details on this, or do you have any questions?

Here are 5 related questions for further exploration:

1. How would the time change if the well were only 100 meters deep?
2. What if the stone were thrown downward with an initial velocity? How would this affect the depth calculation?
3. How does air resistance affect the stone’s fall, and would it change the result significantly?
4. If the stone were dropped on a different planet with a gravity of $12 \, \text{m/s}^2$, what would the depth be for the same time?
5. How can you use this method to determine the depth of a well if the stone takes 5 seconds to hit the water?

Tip: Always check if there are any initial velocities or forces acting in problems involving motion under gravity. This can change the formula.