Chapter SH, Problem 6.25EP

To determine

Find thearea of the sail using given data.

Answer to Problem 6.25EP

Thearea of the sail is $80\text{square feet}$ .

Explanation of Solution

Given:

The given modelis $s=150\sqrt{\frac{p}{a}}$ , where $p$ is the pressure of the wind and $a$ is the area of the sail.

Calculation:

  $s=150\sqrt{\frac{p}{a}}$

  $\begin{array}{l}s=75\text{mph}\\ p=20\text{pounds/square feet}\end{array}$

Substitute the value of $s=75$ and $p=20$ in the given model.

  $\Rightarrow 75=150\sqrt{\frac{20}{a}}$

Divide both sides by $150$ .

  $\begin{array}{l}\Rightarrow \frac{75}{150}=\frac{150}{150}\sqrt{\frac{20}{a}}\\ \Rightarrow \frac{1}{2}=\sqrt{\frac{20}{a}}\end{array}$

Squaring both sides.

  $\begin{array}{l}\Rightarrow {\left(\frac{1}{2}\right)}^2={\left(\sqrt{\frac{20}{a}}\right)}^2\\ \Rightarrow \frac{1}{4}=\frac{20}{a}\end{array}$

Multiplying both sides by $a$ .

  $\begin{array}{l}\Rightarrow \frac{1}{4}\cdot a=\frac{20}{a}\cdot a\\ \Rightarrow \frac{1}{4}\cdot a=20\end{array}$

Multiplying both sides by $4$ .

  $\begin{array}{l}\Rightarrow \frac{1}{4}\cdot a\cdot 4=20\cdot 4\\ \Rightarrow a=80\end{array}$

Hence thearea of the sail is $80\text{square feet}$ .