Question

A new unit of length is chosen such that the speed of light in a vacuum is unity. What is the distance between the sun and the earth in terms of the new unit if light takes 8 minutes and 20 seconds to cover this distance?

Answer 1

Given:

The speed of light in vacuum $=1unit=1\raisebox{1ex}{$lengthunits$}\!\left/ \!\raisebox{-1ex}{$sec$}\right.$

Time taken by the light to cover the distance from the sun to the earth $=8min20s(500s)$

Finding the distance between the sun and the earth:

We know that $dis\tan ce=speed\times time$

By substituting the given values, we get

$$\begin{gathered} dis\tan ce=1\frac{lengthunits}{sec}\times 500sec \\ =500lengthunits \end{gathered}$$

Hence, the distance between the earth and the sun is 500 length units.