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QUESTION

# The speed of light in a vacuum is 2.998 xx 10^8 "m/s". (a) What is its speed in kilometers per hour (km/h)? (b) What is its speed in miles per minute (mi/min)?

For part (a): c = 1.079 * 10^(9)"km/h" For part (b): c = 1.118 * 10^7"mi/min"

To solve this problem you need to be familiar with several conversion factors. More specifically, you need to know that

"1 km" = 10""^3"m"

"1 h" = "60 min" " "and " ""1 min" = "60 s"

"1 mile" = "1.609344 km"

SO, for part (a), you need to go from meters to kilometers and from seconds to minutes, then to hours.

2.998 * 10^(8)color(red)(cancel(color(black)("m")))/color(red)(cancel(color(black)("s"))) * "1 km"/(10^3color(red)(cancel(color(black)("m")))) * (60color(red)(cancel(color(black)("s"))))/(1color(red)(cancel(color(black)("min")))) * (60color(red)(cancel(color(black)("min"))))/(1color(red)(cancel(color(black)("h")))) = 10792.8 * 10^(5)"km/h"

Rounded to four , the number of sig figs you gave for the speed of light in meters per second, the naswer will be

c = color(green)(1.079 * 10^(9)"km/h")

Now for part (b). Now you need to go from meters to kilometers, then to miles, and from seconds to minutes.

2.998 * 10^(8)color(red)(cancel(color(black)("m")))/color(red)(cancel(color(black)("s"))) * (1color(red)(cancel(color(black)("km"))))/(10^3color(red)(cancel(color(black)("m")))) * "1 mile"/(1.609344color(red)(cancel(color(black)("km")))) * (60color(red)(cancel(color(black)("s"))))/"1 min" = 111.77 * 10^(5)"mi/min"

Once again, round the answer to four sig figs

c = color(green)(1.118 * 10^7"mi/min")