Chapter 7.3, Problem 65PPS

To determine

The kilometers traveled by light in a day, a week, a month and a year.

Answer to Problem 65PPS

In 24 hours:

  $432\times {10}^4\text{ kilometers}$

In 1 week:

  $3024\times {10}^4\text{ kilometers}$

In 30 days:

  $12960\times {10}^4\text{ kilometers}$

In 365 days:

  $157680\times {10}^4\text{ kilometers}$

Explanation of Solution

Given:

The speed of light is:

  $3\times {10}^8\text{ meter per second}$

Calculation:

The speed of light in kilometers per hour will be:

  $\begin{array}{l}=\frac{3\times {10}^8}{1000}\times \text{60 kilometer per hour}\\ =\frac{3\times {10}^8}{{10}^5}\times \text{60 kilometer per hour}\\ =180\times {10}^{8-5}\text{ kilometer per hour}\\ =180\times {10}^3\text{ kilometer per hour}\\ =18\times {10}^4\text{ kilometer per hour}\end{array}$

In 24 hours:

  $\begin{array}{l}=\left(18\times {10}^4\text{ kilometer per hour}\right)\times \text{24}\\ \text{= }432\times {10}^4\text{ kilometers}\end{array}$

In 1 week:

  $\begin{array}{l}\text{= }\left(432\times {10}^4\text{ kilometers}\right)\times \text{7}\\ \text{=}3024\times {10}^4\text{ kilometers}\end{array}$

In 30 days:

  $\begin{array}{l}\text{= }\left(432\times {10}^4\text{ kilometers}\right)\times \text{30}\\ \text{=}12960\times {10}^4\text{ kilometers}\end{array}$

In 365 days:

  $\begin{array}{l}\text{= }\left(432\times {10}^4\text{ kilometers}\right)\times \text{365}\\ \text{=}157680\times {10}^4\text{ kilometers}\end{array}$