Chapter 1, Problem 1VSC

To determine

Distance between the two photos in order to show the distance between Earth and the Moon on the scale of $\left(1\text{cm}=4000\text{km}\right)$.

Answer to Problem 1VSC

Solution:

In order to show the distance between Earth and the Moon you need to place the photos about 1 meter apart (about the length of your arm). Therefore option (b) is correct.

Explanation of Solution

Given:

Distance between the Earth and the Moon, $x=384,000\text{km}$

Scale, $\left(1\text{cm}=4000\text{km}\right)$.

Calculation:

As we know the distance between the Earth and the Moon is $384,000\text{km}$, The distance on the desired scaled of $\left(1\text{cm}=4000\text{km}\right)$ is calculated as

$\begin{array}{c}y=384000\left(\text{km}\right)\times \frac{1\text{cm}}{1\text{cm}}\\ =384000\left(\text{km}\right)\times \frac{1\text{cm}}{4000\left(\text{km}\right)}\left(\because 1\text{cm}=4000\text{km}\right)\\ =96\text{cm}\\ \approx \text{1}\text{m}\end{array}$

Hence, the photo should be 1 m apart (about the length of your arm) in order to show the distance between the earth and the moon on the scale of $\left(1\text{cm}=4000\text{km}\right)$.

Conclusion:

The distance between the photos should be $1\text{m}$ in order to show the distance between the earth and the moon on the scale of $\left(1\text{cm}=4000\text{km}\right)$.