Question #5993b

1 Answer
Aug 30, 2015

Answer:

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

Explanation:

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 sig figs, 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")#