Question

Light travels at approximately `3.0*10^8` `m``/``sec`, How far does light travel in one week?

Answer 1

`1.8 × 10^14\ "m"`

Explanation:

Speed is given by

`"Speed" = "Distance"/"Time"`

From above

`"d = Speed × Time"`

`color(white)("d") = 3 × 10^8\ "m/s" × "1 week"`

`color(white)("d") = 3 × 10^8\ "m/s" × 1 cancel"week" × "7 days"/(1 cancel"week")`

`color(white)("d") = 3 × 10^8\ "m/s" × 7 cancel"days" × "24 hrs"/(1 cancel"day")`

`color(white)("d") = 3 × 10^8\ "m/s" × 7 × 24 cancel"hrs" × "60 min"/(1 cancel"hr")`

`color(white)("d") = 3 × 10^8\ "m/s" × 7 × 24 × 60 cancel"min" × "60 s"/(1 cancel"min")`

`color(white)("d") = 3 × 10^8\ "m"/cancel"s" × 7 × 24 × 60 × 60 cancel"s"`

`color(white)("d") = 3 × 10^8\ "m" × 604800`

`color(white)("d") = 1814400 × 10^8\ "m"`

`color(white)("d") = 1.8144 × 10^14\ "m"`

Light travelled `1.8 × 10^14\ "m"` (in 2 significant figures) in a week.

Answer 2

`~~1.8144 xx 10^14 " "m/("week")`

Explanation:

Given: Light travels at `~~ 3.0 xx 10^8 m/s`

Use dimensional analysis to find the answer:

`3.0 xx 10^8 m/s xx (60" s")/"min" xx (60 " min")/h xx (24 " " h)/("day") xx (7 " days")/("week")`

`= 3.0 (60)^2(24)(7) xx 10^8 = 1,814,400 xx 10^8`

`= 1.8144 xx 10^6 xx 10^8`

`= 1.8144 xx 10^(6+8)`

`= 1.8144 xx 10^14" "m/("week")`