Question

Need help with Astronomy problem. It takes light 8.3 minutes to travel from the Sun to the Earth. How long would it
take an airplane traveling at 340 m/s (the speed of sound in air) to make the same trip? (the
speed of light is 3 X 108 m/s) To receive full credit, solve this problem using ratios.

Answer 1

For light, to travel the distance from Sun to Earte, namely s, we need a time t
\[s=c\cdot t\]If we use a new velocity v, we will need another time T,
\[s=v\cdot T\]We now take the ratios,
\[s/s=(c/v)\cdot (t/T)\Rightarrow T=\frac{c}{v}\cdot t\Rightarrow\frac{3\cdot10^8}{340}=8.82\cdot10^5 t\]
So, it takes approximately 882000 times the time that light uses.