Question

A light year is the distance light (speed=2.99x10^8 m/s) travels in 1.00 light year. (A) how many meters are there in a light year? (B) an astronomical unit (AU) is the average distance from the sun to earth, 1.50x10^8 km. how many AU are there in 1 light year? (C)what is the speed of light in an AU/h?

I already did the first one but I need help with a and b

Answer 1

\(\bf 2.99\times10^8 \implies 299000000\frac{m}{second}\\
\color{blue}{\textit{so how many per year?}}\\
299000000 \times 60 \implies \frac{m}{minute}\\
299000000 \times 60 \times 60 \implies \frac{m}{hour}\\
299000000 \times 60 \times 60 \times 24 \implies \frac{m}{day}\\
299000000 \times 60 \times 60 \times 24 \times 365 \implies \frac{m}{year}
\)

Answer 2

Thanks but what about the last one... I'm sorry I just need help

Answer 3

well, use the m/hour value to get how many meters per hour
divide that by 1000, because

1000 meters = 1 kilometer

and then divide by 1.5x10^8

\(\bf 299000000 \times 60 \times 60 \implies \frac{m}{hour}\\
\color{blue}{1.5\times 10^8 \implies 150000000}\\
299000000 \times 60 \times 60 \div 1000 \div 150000000 \frac{AU}{hour}\)