A girl drops a stone into a dry well and hears it hit the bottom 2.4 s later…

Step 1. The equation. $t + \dfrac{4.9t^2}{330} = 2.4$, so $4.9t^2 + 330t - 792 = 0$.

Step 2. Fall time. $\sqrt{108900\ \text{m}^2/\text{s}^2 + 15523\ \text{m}^2/\text{s}^2} = 352.7\ \text{m/s}$, so $t = \dfrac{-330\ \text{m/s} + 352.7\ \text{m/s}}{9.8\ \text{m/s}^2} = 2.32\ \text{s}$.

Step 3. Depth. $h = 4.9\ \text{m/s}^2 \times (2.32\ \text{s})^2 = 26.4\ \text{m}$.

Step 4. Ignoring the sound. $4.9\ \text{m/s}^2 \times (2.4\ \text{s})^2 = 28.2\ \text{m}$.