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The speed of light is 3.00 times 10^8 m / s. How fast is this in miles per hour (miles / h)?

Question:

The speed of light is {eq}3.00 \times 10^8 \ m / s {/eq}. How fast is this in miles per hour {eq}(miles / h) {/eq} ?

Speed of Light:

The speed of light is regarded as the speed limit of our universe. According to the concepts brought forward by relativity, the speed of light cannot be exceeded by any object in the universe. Moreover, just approaching more than 1% of this speed produces some weird effects as put forward by relativity. We get to experience phenomena such as time dilation and length contraction as we approach the speed of light.

Answer and Explanation:


Given:

  • {eq}\displaystyle c = 3\ \times\ 10^8\ m/s {/eq} is the speed of light


Here we note the following conversion factors:

  • {eq}\displaystyle 1\ min = 60\ s {/eq}
  • {eq}\displaystyle 1\ h = 60\ min {/eq}
  • {eq}\displaystyle 1\ km = 0.6214\ mi {/eq}
  • {eq}\displaystyle 1\ km = 1000\ m {/eq}

In 1000 meters, we have 0.6214 miles. We thus now convert our units:

{eq}\displaystyle c = 3\ \times\ 10^8\ \frac{m}{s}\left(\frac{0.6214\ mi}{1000\ m} \right)\left(\frac{60\ s}{1\ min} \right)\left(\frac{60\ min}{1\ h} \right) {/eq}

We cancel similar units:

{eq}\displaystyle c = 3\ \times\ 10^8\ \frac{\require{cancel}\cancel{m}}{\require{cancel}\cancel{s}}\left(\frac{0.6214\ mi}{1000\ \require{cancel}\cancel{m}} \right)\left(\frac{60\ \require{cancel}\cancel{s}}{1\ \require{cancel}\cancel{min}} \right)\left(\frac{60\ \require{cancel}\cancel{min}}{1\ h} \right) {/eq}

We thus get:

{eq}\displaystyle \boxed{c = 6.71\ \times\ 10^{11}\ mi/h} {/eq}


Learn more about this topic:

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Common Unit Conversions

from Business 110: Business Math

Chapter 1 / Lesson 10
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