Chapter 9, Problem 14STP

To determine

To find the scale of the model.

Answer to Problem 14STP

  $1:2400$

Explanation of Solution

Given:

The actual length of Bridge is $9000$ feet and the length of model is $45$ inches.

Calculation:

Scale factor of the model can be calculated as follows-

  $\begin{array}{l}k=\frac{\text{model length}}{\text{actual length}}\\ k=\frac{45\text{ inch}}{9000\text{ feet}}\\ k=\frac{45}{9000\times 12}\\ k=\frac{1}{2400}\end{array}$

To determine

To find the width of model if actual width is $90$ feet.

Answer to Problem 14STP

  $\text{0}\text{.45 inch}$

Explanation of Solution

Given:

The actual length of Bridge is $9000$ feet and the length of model is $45$ inches.

Calculation:

The model width can be calculated as follows-

  $\begin{array}{l}\text{model width}=k\times \text{actual width}\\ \text{=}\frac{1}{2400}\times 90\text{ feet}\\ \text{=}\frac{3}{80}\times 12\text{ inch}\\ \text{=0}\text{.45 inch}\end{array}$

To determine

To find the height of the actual tower above the road way.

Answer to Problem 14STP

  $500\text{ feet}$

Explanation of Solution

Given:

The model of the tower is $2.5$ inches above the roadway.

Calculation:

The height of the actual tower above the roadway can be calculated as follows-

  $\begin{array}{l}\text{actual height}=\frac{\text{model height}}{k}\\ =\frac{2.5\text{ inch}}{\frac{1}{2400}}\\ =\frac{2400\times 2.5}{12}\text{ feet}\\ =500\text{ feet}\text{.}\end{array}$