Chapter 7.7, Problem 17PPS

a.

To determine

To find the approximate height of the rocket.

Answer to Problem 17PPS

  $84\text{ ft}$

Explanation of Solution

Given:

Peter bought a $\frac{1\text{ in}}{12\text{ ft}}$ scale model of the Mercury-Redstone rocket. The height of the model is $50$ inches.

Calculation:

Let $x$ be the height of the rocket.

It is known that the scale is defined by the following formula-

  $\begin{array}{l}\text{scale}=\frac{\text{model length}}{\text{actual length}}\\ \frac{1\text{ in}}{12\text{ ft}}=\frac{\text{7 in}}{x\text{ ft}}\\ \Rightarrow x=7\times 12\\ \Rightarrow x=84\text{ ft}\end{array}$

b.

To determine

To find the diameter of the model to the nearest half inch.

Answer to Problem 17PPS

The diameter of the model is $0.5\text{ inch}$ .

Explanation of Solution

Given:

Peter bought a $\frac{1\text{ in}}{12\text{ ft}}$ scale model of the Mercury-Redstone rocket. The diameter of the rocket is $70$ inches.

Calculation:

Change $12$ feet to inches so you have a unit-less scale factor.

  $12ft=12\times 12\text{ inch}=\text{144 inch}$

Let $x$ be the diameter of the model.

Now, apply the proportion rule of similarity as follows-

  $\begin{array}{l}\frac{1}{144}=\frac{x}{70}\\ \Rightarrow x=\frac{70}{144}\\ \Rightarrow x\approx 0.5\text{ inch}\end{array}$