Question 5993b

Aug 30, 2015

For part (a): $c = 1.079 \cdot {10}^{9} \text{km/h}$
For part (b): $c = 1.118 \cdot {10}^{7} \text{mi/min}$

Explanation:

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

$\text{1 km" = 10""^3"m}$

$\text{1 h" = "60 min" " }$and $\text{ ""1 min" = "60 s}$

$\text{1 mile" = "1.609344 km}$

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

$c = \textcolor{g r e e n}{1.079 \cdot {10}^{9} \text{km/h}}$

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

$c = \textcolor{g r e e n}{1.118 \cdot {10}^{7} \text{mi/min}}$