# Applications Using Linear Models

## Solve story problems using linear equations

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Tracking the Storm

Credit: Victor Gumayunov
Source: http://www.flickr.com/photos/gumayunov/2686913266/

Why does thunder always come after lightning? Have you ever counted the number of seconds between lightning and thunder to see how far away a storm was? If you have, then you were doing a linear-relationship math problem using time and the speed of sound!

#### Why It Matters

Seeing a lightning bolt in the sky and hearing a boom of thunder are two results of the same storm event. This event is a huge electrical discharge between charged regions in the clouds and on the ground. So why do we see lightning before we hear it? It's because light travels a whole lot faster than sound. In just one second, light travels 186,282 miles, while sound travels only about \begin{align*}\tfrac{1}{5}\end{align*}of a mile. If we assume that the extraordinary speed of light allows us to see lighting at almost the instant it occurs, then we can use the linear relationship between distance and time to estimate how far away a storm is, and to determine if we might want to run for cover!

Credit: Search Engine People Blog
Source: http://www.flickr.com/photos/sepblog/4072462666

Imagine that you saw a flash of lightning and then counted one-mississippi, two-mississippi, three-mississippi? BOOM! How far away did the lightning strike? Well, if the sound of thunder travels at an approximate rate of 0.2 miles per second, and it took 3 seconds to get to you, then it must have traveled a journey of about \begin{align*}0.2\times3=0.6\end{align*} miles. Notice the linear relationship between time and distance: 5 seconds is 1 mile, 10 seconds is 2 miles, and so on.

See for yourself: http://www.lightningsafety.noaa.gov/distance.htm

#### Explore More

http://www.srh.noaa.gov/jetstream/lightning/thunder.htm#distance

1. Is the speed of sound always the same?
2. What kind of relationship do atmospheric temperature and the speed of sound have?

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