Question

Knowing the speed of light (3x10m/s), calculate how long a

light year is in meters! (using dimensional analysis)

Answer 1

9.5 x 10^15 meters per year

Step-by-step explanation:

So, you have:

`(300,000,000)/(1) (meters)/(second)`

We want the amount of meters light travels in one year. There are 3600 seconds in 1 hour, 24 hours in 1 day, and 365 days in a year. Using these conversion factors, we can set up some nice cancellations:

`(300,000,000)/(1) (meters)/(second)(3600)/(1) (seconds)/(hour) (24)/(1) (hours)/(day) (365)/(1) (days)/(year)`

Seconds will cancel, hours will cancel, days will cancel. We have meters per year:

`300,000,000*3600*24*365(meters)/(year) =9.5x10^(15)(meters)/(year)`