Chapter 15, Problem 81A

To determine

To calculate: The time taken to hear the stone hit the bottom of the well.

Answer to Problem 81A

The time taken to hear the stone hit the bottom of the well = $\underset{\_}{\text{5}\text{.36 s}}$ .

Explanation of Solution

Given:

Depth of the well = $\text{122}\text{.5 m}$

Formula used:

Distance for a free fall is given by,

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

Where $g$ is acceleration due to gravity, and $t$ is the time taken.

Time taken for the sound to come back up is given by,

$t=\frac{d}{v}$

Where $d$ is distance and $v$ is velocity.

Calculation:

The time taken to hear the stone hit the bottom of the well = Time taken for the stone to reach the bottom of the well $+$ Time taken for the sound of the stone to come back up.

Time taken for the stone to reach the bottom of the well is calculated as:

$\begin{array}{l}t=\sqrt{\frac{2d}{g}}\\ \text{ =}\sqrt{\frac{2\times 122.5\text{ m}}{9.8\text{ m/s}}}\text{ [g}=\text{9}{\text{.8 m/s}}^2]\\ \text{ = 5 s}\end{array}$

Time taken for the sound of the stone to come back up is calculated as:

$\begin{array}{l}t=\frac{d}{v}\\ \text{ =}\frac{122.5}{343}\\ \text{ =0}\text{.36 s}\end{array}$

The time taken to hear the stone hit the bottom of the well = $\text{5+0}\text{.36 = 5}\text{.36 s}$ .

Conclusion:

The time taken to hear the stone hit the bottom of the well = $\underset{\_}{\text{5}\text{.36 s}}$ .