Chapter 8.1, Problem 16P

To determine

To find the distance an object falls before its speed is $\text{80 ft/s}$ .

Answer to Problem 16P

The distance it must fall is $\text{100 ft}$ .

Explanation of Solution

Given information:

The given statement is:

“The speed of an object falling from rest is directly proportional to the square root of the distance the object has fallen. When an object has fallen $\text{36 ft}$ , its speed is $\text{48 ft/s}$ . How much farther must it fall before its speed is $\text{80 ft/s}$ ?”

Calculation :

The distance can be calculated by:

  $\begin{array}{l}\frac{y_1}{\sqrt{x_1}}=\frac{y_2}{\sqrt{x_2}}\\ \frac{48}{\sqrt{36}}=\frac{80}{\sqrt{x_2}}\\ \sqrt{x_2}=\frac{80\times \sqrt{36}}{48}\\ \sqrt{x_2}=\frac{80\times 6}{48}\\ \sqrt{x_2}=10\\ x_2={10}^2\\ x_2=100\end{array}$

Hence, the distance it must fall is $\text{100 ft}$ .