Question

How far does light travel in the following time spans: 4 days and 8 years?

Answer 1

Hint: To calculate the distance travelled by light in the given time period, we will make use of speed of light in vacuum, that is equal to $3\times {{10}^{8}}m/s$ . Now, to calculate the distance travelled by light in a straight line path, we will use: Distance traversed by light is equal to Speed of light (which is a known quantity) multiplied by time duration (as mentioned in the question).

Complete answer:
Let the speed of light in vacuum be $(u)m/s$ .
We know that the speed of light in vacuum is equal to $3\times {{10}^{8}}m/s$ .
$\Rightarrow u=3\times {{10}^{8}}m/s$
Now, in the first case the time duration is 4 days. Let us first convert it into seconds. Then:
Since, 1 day has 24 hours , 4 days is:
$\begin{align}
  & =4\times 24hrs \\
 & =96hrs \\
\end{align}$
Since, every hour has 60 minutes and every minute has 60 seconds, therefore 1 hour has:
$\begin{align}
  & =60\times 60s \\
 & =3600s \\
\end{align}$
Thus, 96 hours has:
$\begin{align}
  & =96\times 3600s \\
 & =345600s \\
\end{align}$
Therefore, the distance travelled by light in 4 days is equal to:
$\begin{align}
  & =3\times {{10}^{8}}\times 345600m \\
 & =1036800\times {{10}^{8}}m \\
 & =1.0368\times {{10}^{14}}m \\
\end{align}$
Hence, the distance travelled by light in 4 days is $1.0368\times {{10}^{14}}m$ .
Now, for the second case we have time duration as 8 years.
Since, every year has 365 days. 8 years is equal to:
$=8\times 365$
$=2920$ days
Since, we have calculated the distance travelled by light in 4 days (say D), therefore the distance travelled by light in 2920 days will be equal to:
$=\left( \dfrac{2920}{4} \right)\times D$
Where,
$\Rightarrow D=1.0368\times {{10}^{14}}m$
Therefore, distance travelled by light in 8 years is equal to:
$\begin{align}
  & =\left( \dfrac{2920}{4} \right)\times 1.0368\times {{10}^{14}}m \\
 & =730\times 1.0368\times {{10}^{14}}m \\
 & =7.56864\times {{10}^{16}}m \\
\end{align}$
Hence, the distance travelled by light in 8 years is $7.56864\times {{10}^{16}}m$ .

Note:
In this problem, we saw the use of some trivial values of terms like the speed of light, how many seconds there are in an hour or in a day or even in a year. So, these questions come in easy categories of problems. So, the only place that has a chance of error is calculation. So, we need to be very careful in these lengthy calculations.