Chapter 12.8, Problem 14OE

To determine

To Describe: Translate the statement into formula:

The wind resistance, $R$ , of an object is varies jointly as the area , $A$ , of its surface facing the wind and the square of the speed, $s$ , of the wind.

Answer to Problem 14OE

The formula of the statement is $R=kA{s}^2$ .

Explanation of Solution

Given information:

Translate statement to formula:

The wind resistance, $R$ , of an object is varies jointly as the area , $A$ , of its surface facing the wind and the square of the speed, $s$ , of the wind.

Use $K$ as constant.

Consider the statement,

The wind resistance, $R$ , of an object is varies jointly as the area , $A$ , of its surface facing the wind and the square of the speed, $s$ , of the wind.

Here if a variable varies directly as he product of two or more other variables the resulting relationship is a joint variation.

As , $R$ ,varies jointly as the area, $A$ and the square of speed, $s$ .

  $R$ is directly to the distance, $A$ .

  $R\alpha A$ .

Then $R$ is inversely as its square of speed, $s$ .

  $R\alpha s^2$

From both of the equations:

  $\begin{array}{c}R\alpha A\\ R\alpha s^2\\ R\alpha A{s}^2\end{array}$

Same as above,

Here,

  $R\alpha A{s}^2$

For replacing $\alpha$ apply constant $K$ .

  $\begin{array}{l}R\alpha A{s}^2\\ R=KA{s}^2\end{array}$

Thus, the formula is: $R=kA{s}^2$ .