Mike+Alg

Mike Thiele Jake Bohman Christian Colaco Algebra 1 4A = __**Radicals Applied :Roller Coasters**__ =  A great way to demonstrate the use of radicals in the real world is a roller coaster. Roller coasters usually start with a massive incline and then have a steep drop. The m omentum from the drop carries the coaster throughout ride and no other force is used.

To calculate the speed of the drop of a roller coaster, the equation, v=√2gh **,** must be used. “V” is speed, “g” is the acceleration from gravity, which is 32 ft./s2, and “h,” the height from which the coaster is dropped.

The attraction, Alpengeist at Busch Gardens, is a great example of this concept. It drops passengers from a height of 195 feet at a speed of approximately 112 ft./s, or 76 mi/h. The speed was found very simply.

First, plug the height of the coaster, 195 feet, where “h” is. Put 32 in for “g” because that is the rate of gravity. The final step is to solve the equation as follows.

v=√2(32)(195) =√12480 =111.7 (112) ft/s

However, this speed differs from the speed listed on the website for Busch Gardens. This is because the number is just an average speed.

A second example of this concept is the coaster Loch Ness Monster in Busch Gardens. This one drops at a height of 114 at a speed of 85 ft./s. This was found the same way as Alpengeist.

V=√2(32)(114) =√7296 =85.4 (85) ft./s

When comparing the two coasters' speeds, both are dropping and are not propelled by any other force besides gravity. The characteristic that determines the speed of the drop must be the height.

To help explain the concept of the speed of a roller coaster, click on the link below.

@http://www.worsleyschool.net/science/files/roller/coasters.html