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# Linear, Exponential, and Quadratic Models

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Practice Linear, Exponential, and Quadratic Models
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Airplanes in Flight

Credit: Makaristos
Source: http://commons.wikimedia.org/wiki/File:N575UA-2008-09-13-YVR.jpg
License: CC BY-NC 3.0

When ready for takeoff, the average commercial airplane weighs about 830,000 pounds. How is it able to fly if it is so heavy? Can quadratic equations help to solve this aviation mystery?

#### News You Can Use

The airplane’s wing can be described as an airfoil. When air hits it, the air splits. The faster air moves over the top of the wing’s surface and the slower air moves along the lower portion of the wing’s surface. Air speed and pressure are inversely related, so the higher the velocity of the air, the lower the pressure. Airplanes can fly due to Bernoulli’s Principle.

Credit: epSos.de
Source: http://www.flickr.com/photos/epsos/7928294800/
License: CC BY-NC 3.0

So how does Bernoulli’s Principle work? As the wing of a plane passes through the air, more air flows over the top of the wing than under the bottom of the wing. The shape of airplane wings has a lot to do with why more air travels over the top of the wing. As the air moves it creates more pressure under the wing than above it, causing the airplane’s wing to be pushed up and lifted. Bernoulli’s equation to determine this phenomenon looks a lot like the standard quadratic equations you may see in class:

$\frac{u^2}{2}+P=h$

Watch an animation of Bernoulli’s Principle: https://www.youtube.com/watch?v=bv3m57u6ViE

#### Explore More

Check out the following link to see what other phenomena can be modeled using Bernoulli’s Principle. Then answer the questions below.

1. What does the flight of airplanes, curve balls, and ping pong balls in a funnel have in common?
2. How is the ping pong ball able to stay suspended in the air?
3. How does a curve ball curve according to Bernoulli’s Principle?

### Image Attributions

1. [1]^ Credit: Makaristos; Source: http://commons.wikimedia.org/wiki/File:N575UA-2008-09-13-YVR.jpg; License: CC BY-NC 3.0
2. [2]^ Credit: epSos.de; Source: http://www.flickr.com/photos/epsos/7928294800/; License: CC BY-NC 3.0

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