Question

At a certain location on earth the sun appears to cross the meridian at 12 noon. At what angular position was the sun when it emitted the observed light? (The sun is at 92 $\times$ 10$^6$ mi from each of light=186,000 mi/s)

Answer 1

Hint: In this question first we will convert time in hours which is given in seconds. After that we will calculate the angular position for 24 hours. Likewise we will calculate for an hour. The time we calculated is then used for the value given in the question and thus the angular position of the sun can be determined.

Complete answer:
Given that the sun crosses the meridian at a particular location on earth at 12 noon. We need to find the angular position of the sun.
Given speed of light=1860000 mi/s
Time is given by
\[\begin{align}
 & =\dfrac{52\times {{10}^{6}}}{186000} \\
 & =5\times {{10}^{2}}\sec \\
\end{align}\]
We will convert this time from second to hours \[=\dfrac{5\times {{10}^{2}}}{60\times 60}hours\]
In 24 hours \[=360\]
In 1 hour \[=\dfrac{360}{24}\]
In \[\dfrac{5\times {{10}^{2}}}{60\times 60}\]hours= \[\dfrac{360}{24}\times \dfrac{5\times {{10}^{2}}}{60\times 60}\] \[=2.06{}^\circ \] cast of meridian
Therefore at \[2.06{}^\circ \] cast of meridian the sun observes the light.

Thus option D is correct.

Additional information:
Some geographic terms play an important role for understanding these topics such as latitude, longitude etc. When we measure our position from north to south direction on earth then it is called latitude. When we measure our position from east to west direction on earth then it is called longitude.

Note:
Meridian is a geographic term used to imagine a great circle on the earth’s surface. It is half of the great circle terminated by the North pole and South pole. It is measured in angular degrees. This can also be understood as a line joining the two poles at right angles. It is used to represent longitude. All longitudes have their own importance. We can also use this to navigate whether we are going east or west.