Question

The conversion factor relating miles to meters is 1mile=1610m. The speed of light is 3.00×108 m/s. How fast is this in miles per hour (miles/h)?

Answer 1

The speed of light is equal to $6.71 \times 10^8 \frac{mi}{h}$ or $3.00 \times 10^8 \frac{m}{s}$.

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:

1. Convert meters to miles.
2. 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:

$speed \ of \ light \ =3.00 \times 10^8 \ \frac{m}{s} \ (\frac{1 \ mi}{1610 \ m}) \ (\frac{60 \ s}{1 \ min}) \ (\frac{60 \ min}{1 \ h})\\speed \ of \ light \ = 670,807,453.4 \frac{mi}{h}$

Since the answer must be expressed with only 3 significant figures, the final answer is:

$\boxed {\boxed {speed \ of \ light \ = 6.71 \times 10^8 \ \frac{mi}{h}}}$

Learn More

1. Learn more about Metric Conversion brainly.com/question/1600704
2. Learn more about SI units brainly.com/question/10928588
3. Learn more about dimensional analysis brainly.com/question/1557970

Keywords: unit conversion, dimensional analysis

Answer 2

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