Step-by-step explanation:
the speed of the light is
![v=3*10^8\text{ m/s}](https://img.qammunity.org/2023/formulas/physics/college/77yql4bmxnd8ozezl2ko3i19207h2zs8lh.png)
the time in a year is
![\begin{gathered} t=365\text{ days}*24\text{ hours}*60\text{ minutes}*60\text{ seconds} \\ \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/1b8p6imt2mom82obnkfdibrs6h28d31vyw.png)
the distance traveled by the light is
![d=v\text{ t}](https://img.qammunity.org/2023/formulas/physics/college/uxdumwjd72fn6a4c3vpo4fc6cpe3r5t8r0.png)
Plugging all the values in the above relation, we get
![\begin{gathered} d=365*24*60*60\text{ s}*3*10^8\text{ m/s} \\ d=946080*10^(10)\text{ m} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/cpgq21so096pqbe04z4phgfl1v7iknzd4q.png)
now convert this into miles.
![1\text{ m=0.000621 miles}](https://img.qammunity.org/2023/formulas/physics/college/750bgp40sq0jn1uce5ql7gf0rn8fezf5ip.png)
now the distance is,
![\begin{gathered} d=946080*0.000621*10^(10)\text{ miles} \\ d=587.51*10^(10)\text{ miles} \\ d=\text{ 6 billion miles} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/behtl8czevtrrf72pzrp5wzinip2qim1ul.png)
Thus, the distance traveled by the light in a year is 6 billion.