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Radical Equations

Find the roots of basic equations containing roots

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Driving on Water

Credit: Creativity103
Source: http://www.flickr.com/photos/creative_stock/3526479593
License: CC BY-NC 3.0

You’re driving on the interstate, keeping up with the speed of traffic. Suddenly, you’re hit with torrential rains. You can’t feel the road beneath your tires any more. You can’t steer. Your brakes aren’t working like they normally do. What just happened?


When a car hydroplanes, it drives on top of a layer of water. Since it has lost contact with the roadway, it can’t easily change direction or stop. Instead, it skims the surface, much like a speedboat. Engineers have determined an equation that predicts when hydroplaning will occur: \begin{align*}v=10.35 \sqrt{p}\end{align*}, where \begin{align*}v\end{align*} is the speed (in miles per hour) at which a car will hydroplane and \begin{align*}p\end{align*} is the tire pressure (in PSI). This means that cars with underinflated tires are more likely to hydroplane. Cars cannot hydroplane unless the water on the road is deeper than the tread on its tires. Hydroplaning usually occurs at high speeds on roads with deep puddles. This is one reason why your parents and driving instructors tell you to slow down when you’re driving in the rain.

Credit: thienzieyung
Source: http://www.flickr.com/photos/thienzieyung/5778997966
License: CC BY-NC 3.0

Since hydroplaning drivers are unable to control their cars, they can cause serious accidents on busy roads. To avoid hydroplaning, slow down when roads are wet. Learn to use a tire gauge and check your tires on a regular basis. If your tire pressure is low, add air. Finally, check your tire treads. Worn tires are more likely to hydroplane than new tires. If your tread is too low, replace your tires.

See for yourself: http://www.youtube.com/watch?v=spaOeDD3rgo

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Mike is driving a Toyota Camry. He’s inflated his tires to the dealer-recommended level of 32 PSI. At what speed will Mike’s car start hydroplaning? With what tire pressure would his car start hydroplaning at 45 miles per hour?

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  1. [1]^ Credit: Creativity103; Source: http://www.flickr.com/photos/creative_stock/3526479593; License: CC BY-NC 3.0
  2. [2]^ Credit: thienzieyung; Source: http://www.flickr.com/photos/thienzieyung/5778997966; License: CC BY-NC 3.0

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