Respuesta :
Converting from one units to another set of units, a conversion factor is needed. For this problem, the conversion factor would be 1 mile = 1610 m. We convert the value of speed of light from meters/second to miles/hour as follows:
3 x 10^8 m/s (1 mile / 1610 m) ( 60 s / 1 min ) ( 60 min / 1 hr ) = 6.71 x 10^8 miles / hr
3 x 10^8 m/s (1 mile / 1610 m) ( 60 s / 1 min ) ( 60 min / 1 hr ) = 6.71 x 10^8 miles / hr
The speed of light is equal to [tex]6.71 \times 10^8 \frac{mi}{h}[/tex] or [tex]3.00 \times 10^8 \frac{m}{s}[/tex].
FURTHER EXPLANATION
This is an example of a unit conversion problem. To solve this, recall the following conversion factors:
1 min = 60 s
1 h = 60 min
The problem also gives the conversion factor for miles to meter:
1 mi =1610 m
To convert the speed of light into the desired unit the following steps must be carried out:
- Convert meters to miles.
- Convert seconds to hours.
These conversion may be done individually or simultaneously in a single dimensional analysis equation. The equation below shows the simultaneous conversion in one equation:
[tex]speed \ of \ light \ =3.00 \times 10^8 \ \frac{m}{s} \ (\frac{1 \ mi}{1610 \ m}) \ (\frac{60 \ s}{1 \ min}) \ (\frac{60 \ min}{1 \ h})\\speed \ of \ light \ = 670,807,453.4 \frac{mi}{h}\\[/tex]
Since the answer must be expressed with only 3 significant figures, the final answer is:
[tex]\boxed {\boxed {speed \ of \ light \ = 6.71 \times 10^8 \ \frac{mi}{h}}}[/tex]
Learn More
- Learn more about Metric Conversion https://brainly.com/question/1600704
- Learn more about SI units brainly.com/question/10928588
- Learn more about dimensional analysis brainly.com/question/1557970
Keywords: unit conversion, dimensional analysis