Chapter 3.3, Problem 55LC

Interpretation Introduction

Interpretation : The speed of light in kilometres/hour is to be expressed.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. Dimensional analysis is a useful method for resolving conversion problems where measurements in one unit are changed to equal measurements.

Answer to Problem 55LC

The speed of light in kilometers/hour is $1.08\times {10}^9\text{km/hr}$ .

Explanation of Solution

Given information :

The speed of light is $3.00\times {10}^{10}\text{cm/s}$ .

It is known that $\text{1}\text{km}\text{=}{\text{10}}^3\text{m}$ , $\text{1m}={10}^2\text{cm}$ , $\text{1}\text{hr}\text{=}\text{60}\text{mins}$ and $\text{1}\text{min}\text{=}\text{60 secs}$ .

The desired conversion is $\text{cm/s}\to \text{km/hr}$ .

The conversion of the speed of light is given as

  $\begin{array}{c}3.00\times {10}^{10}\text{cm/s}\text{=}\frac{3.00\times {10}^{10}\cancel{\text{cm}}}{\cancel{\sec }}\left(\frac{{10}^{-2}\cancel{\text{m}}}{1\cancel{\text{cm}}}\right)\left(\frac{{10}^{-3}\text{km}}{1\cancel{\text{m}}}\right)\left(\frac{60\cancel{\text{sec}}}{1\cancel{\text{min}}}\right)\left(\frac{60\cancel{\text{min}}}{1\text{hr}}\right)\left(\begin{array}{l}\because \text{1}\text{km}\text{=}{\text{10}}^3\text{m, }\\ \text{1m}={10}^2\text{cm,}\\ \text{1}\text{hr}\text{=}\text{60}\text{mins,}\\ \text{1}\text{min}\text{=}\text{60 secs}\\ \end{array}\right)\\ =10800\times {10}^5\text{km/hr}\\ \text{= 1}\text{.08}\times {10}^9\text{km/hr}\end{array}$

Conclusion

The speed of light in kilometers/hour is $1.08\times {10}^9\text{km/hr}$ .