Question

If the speed of light is 3.00x10^8 m/s, what is the length of a light year in meters?

Answer 1

L = ct; where length is L, c is the velocity of light, and t is the time the light travels. This is just distance = velocity X time.

OK, then 1 light-year = L = ct. Given the length unit has "year" in it, how long do you think t is. Yep, t = 1 year. But c = 3 X 10^8 m/sec and not in m/year. So we need to change t = 1 yr to t = ? seconds.

So we just do some unit conversions t = 1 year X 365 day/year X 24 hours/day X 60 min/hour X 60 second/min and that will give you t in seconds. Do you see how? Cancel out the units just like you would cancel out a variable.

Once you have t in seconds invoke L = ct = 3 X 10^8 m/sec X t (in seconds) and that will give you L in meters. And you can verify this by noting the seconds for t cancel the seconds in c, leaving only meters

Answer 2

Thank you so much! You gave me a perfect explanation. God bless yaaa!

Answer 3

Welcome! Any time!