We are tasked with finding the distance to the surface of the water using the given formula:

$\text{Total elapsed time} = t_1 + t_2 = \frac{\sqrt{s}}{4} + \frac{s}{1100}$

where:

• $t_1$ is the time for the object to hit the water, given by $\frac{\sqrt{s}}{4}$.
• $t_2$ is the time for the sound to travel back up the well, given by $\frac{s}{1100}$.
• The total time elapsed is 3.0 seconds.

We will solve this equation for $s$, the distance to the water.

Equation:

$3.0 = \frac{\sqrt{s}}{4} + \frac{s}{1100}$

Let me now solve this equation for $s$.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through solving the equation manually or explain further steps if needed. Let me know if you'd like that!

Here are 5 related questions:

1. How do you manipulate equations involving square roots?
2. What methods can be used to approximate roots of nonlinear equations?
3. How does sound speed impact the travel time calculation in this problem?
4. How would the answer change if the well was deeper?
5. What role does gravity play in determining the object's falling time?

Tip: When solving nonlinear equations, isolating terms with square roots and squaring both sides can help simplify the problem.