Have you ever ridden the Ferris wheel at the State Fair of Texas? If not, it\'s

Question

Have you ever ridden the Ferris wheel at the State Fair of Texas? If not, it's one of the largest Ferris wheels in the United States! Click on the button below to "ride" the Ferris Wheel virtually with two fa patrons Click to Today, we're going to look at some of the math behind the Ferris wheel. In order to get into the Ferris wheel, you first must climb onto a platform several feet above ground level. That platform accommodates for the cars (also called gondolas) to pass by without touching the ground. From that platform, the cars then travel a total of 224 feet in the air. The Ferris wheel has a radius of 106 feet. Using this information, answer the following questions.You can type the answers for questions 1-5, but 6 and 7 should have hand-written work to accompany any answer you provide. Answers without handwritten submissions will not be awarded any points for questions six and seven. 1) What is the diameter of the Ferris wheel? 2) How close do the bottom of the cars come to the ground? 3) Given the information from question 2, about how high is the platform if you walk from the platform into the floor of the gondolas with no gap in height? 4) How high is the center of the Ferris wheel from the ground? In order to answer questions 5 and 6, you'll need to imagine the image of a Ferris wheel superimposed onto a coordinate grid. 5) Assuming the center of the Ferris wheel lies on the y-axis, what would the coordinates of the center of the Ferris wheel be? 6) Use the information from the problem, and your answer to part 5, to write an equation of the wheel. 7) In one rotation, how far does a patron travel while riding the Ferris wheel at the State Fair of Texas?

Explanation / Answer

1. The diameter of the Ferris wheel = 2*radius of the Ferris wheel

=2*106 ft = 212 ft.

2. Total height reached by the Ferris wheel from the ground= 224 ft. = diameter of the Ferris wheel + height of the car when it reaches the bottom

hence, height of the car when it reaches the bottom = 224 ft. - 212 ft. = 12 ft.

3. The height of the platform with no gap in height of the gondolas and the platform = 12 ft.

4. Height of the center of the Ferris wheel = height of the cars when they are at the bottom + radius of the Ferris wheel = 12 ft. + 106 ft. = 118 ft.

5. Assuming the origin to be on the ground,

Coordinates of the center of the Ferris wheel (x,y) = (0,118)

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