# Trigonometry/Worked Example: Ferris Wheel Problem

## The ProblemEdit

### Exam QuestionEdit

*"Jacob and Emily ride a Ferris wheel at a carnival in Vienna. The wheel has a meter diameter, and turns at three revolutions per minute, with its lowest point one meter above the ground. Assume that Jacob and Emily's height above the ground is a sinusoidal function of time , where represents the lowest point on the wheel and is measured in seconds."*

"Write the equation for in terms of ."

[For those interested, the picture is actually of a Ferris wheel in Vienna.]

-Lang Gang 2016

### Video LinksEdit

The **Khan Academy** has video material that walks through this problem, which you may find easier to follow:

## SolutionEdit

Diameter to Radius A diameter circle has a radius of . |

Revolutions per Minute to Degrees per Second A wheel turning at three revolutions per minute is turning per second. Simplifying that's per second. |

Formula for height At our height is . At , we will have turned through , i.e. half a circle, and will be at the top most point of height (because the diameter of the circle is meters). A cosine function, i.e. , is at and at . That's almost exactly opposite to what we want as we want the most negative value at and the most positive at . Ergo, let's use the negative cosine to start our function. At we want , so we will multiply by so that we get . The formula we made is at and at . Multiply by and we get: - , which is at and at
To get make sure reality is not messed up (we can't have negative height ), add and we get - , which is at and at
Our required formula is - .
with the understanding that cosine is of an angle in degrees (not radians). |