Name: Date: Period: Score: First attempt due:

Final corrections due: Math Journal: Ferris Wheels

A Ferris wheel is a non-building structure consisting of a rotating upright wheel with passenger cars (sometimes referred to as gondolas or capsules) attached to the rim in such a way that as the wheel turns, the cars are kept upright, usually by gravity.

The original Ferris wheel at a height of 264 feet was designed and constructed by George Washington Ferris as a landmark for the 1893 World’s Fair in Chicago. The term Ferris wheel later came to be used generally for all such structures. Since the original 1893 Chicago Ferris Wheel, there have been eleven subsequent world’s tallest Ferris wheels. The current record holder is the 550 feet High Roller in Las Vegas, Nevada which opened to the public on March 31, 2014.

At a local carnival, data was gathered for a time vs. height graph of the Ferris wheel. The data was generalized to the following equation that models the height h (in feet) above ground of a seat on the wheel at time t (in seconds). The graph of the ride begins when t = 0 and ends when t =160. 휋 ℎ(푡) = 50 sin ( (푡 − 4)) + 53 16

1] Assuming the ride does not stop once you load the seat, how long does it take to make one revolution of the wheel? Show all work and explain your reasoning.

2] How high above the ground is the loading platform where the rider is seated before the Ferris wheel begins rotating? Show all work and explain your reasoning.

3] What is the highest point a person will go while seated on the Ferris wheel? Show all work and explain your reasoning.

4] What is the lowest point a person will go while seated on the Ferris wheel? Show all work and explain your reasoning.

5] Assuming the ride does not stop once you load, how many seconds does it take until you are at the top of the Ferris wheel for the first time during the ride? Show your work and explain your reasoning.

6] During the first rotation, exactly when will the rider be 100 feet above the ground? Show your work to solve the trig equation. Maintain 4 decimal places of accuracy throughout your work, then round to the nearest second for each time. Include units in your answers.

7] Find the points on the graph for your answers to #5 and 6 and label their coordinates. Are your solutions reasonable? Explain.

8] If the ride lasts 160 seconds and does not stop to change passengers, how many complete revolutions does the Ferris wheel make while the rider is on the ride? Show all work and explain your reasoning.

9] Find ALL of the times when the rider will be 100 feet above the ground during the 160 seconds she is on the ride. Show all work and explain your reasoning.