#1008 Roller Coasters - Designing safe roller coasters requires an understanding of forces, so that engineers know exactly how the trains will move before anything is built.

Ask students to list all of the variables they can see or think of as they watch Futures Channel Movie #1008 Roller Coasters.  Discuss some answers, then ask students to work in pairs or small groups to try to predict what some of the relationships might be among variables that were listed.  Have osme groups explain their results, then focus discussion on the relationship between the speed of a rollercoaster and its height above the ground—specifically that roller coasters speed up as they move downwards.

Tell students that this relationship can be described by this equation, were the velocity, v, is measured in meters per second and h, in meters, represents how far the roller coaster has fallen from the point at the top of its path, where it is barely moving*:

v = square root(19.6h)

(Note: Use the square root symbol when writing this out for students)

Explain that expressions and equations like this, which involve square roots or other roots, are often referred to as irrational, because it is often not possible to express a square root or other root as a ratio of two numbers (that is, there is no way to write a fraction or decimal that it is exactly equal to).  Tell students they will be learning more about irrational expressions and equations in this chapter.