Question

8. The speed of light is 3.0 x 10^10 cm/sec. Express this speed in mi/hr. (You have choices with the scientific notation: multiply scientific notation with the conversion rate, or change the scientific notation to the standard number—but count your zeros very carefully.)I need this in step by step, I’d like explanations to understand too if possible

Answer 1

`671080888\text{ }miles\text{ /hr}`

Step-by-step explanation:

We are to convert from cm/sec to miles per hour

`\text{Given: 3}*10^(10)\text{ cm/sec}`

Using dimensional analysis:

We will break the conversion from cm to miles into smaller units:

from cm to meters, from meters to feet and from feet to miles

100cm = 1meter

0.3048 meters = 1 foot

5280 feet = 1 miles

From seconds to hour:

60 seconds = 1 minute

60 minutes = 1 hour

Let's start with the analysis from cm to miles:

`\begin{gathered} 3*10^(10)\text{ }*(cm)/(\sec)\text{ = }3*10^(10)\text{ }*(cm)/(\sec)*\frac{1\text{ meter}}{100\text{ cm}}*\frac{1\text{ foot}}{0.3048\text{ meters}}*\frac{1\text{ mile}}{5280\text{ f}eet} \\ =\text{ }3*10^(10)*\text{ }(1)/(160934.4)*\frac{\text{miles}}{\sec} \\ =\text{ }(3*10^(10))/(160934.4)*\frac{\text{miles}}{\sec} \end{gathered}`

Next we move to the analysis from seconds to hour:

`\begin{gathered} \frac{3*10^(10)\text{ }}{160934.4}*(miles)/(\sec)\text{ = }\frac{3*10^(10)\text{ }}{160934.4}*(miles)/(\sec)*\frac{60\text{ sec}}{1\text{ min}}*\frac{60\text{ min}}{1\text{ hour}} \\ =\text{ }\frac{3*10^(10)\text{ }}{160934.4}*(3600)/(1)*\frac{miles}{\text{hour}} \\ =\text{ }\frac{10800*10^(10)\text{ }}{160934.4}*\frac{miles}{\text{hour}} \end{gathered}`
`\begin{gathered} =\text{ }671080888*\frac{miles}{\text{hour}} \\ =\text{ }6.71080888*10^8\frac{miles}{\text{hour}} \end{gathered}`