Question

In order to get into the Ferris wheel, you first must climb onto a platform several feet above ground level. That platform accommodates 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 to 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? 212ft

2) How close to the bottom of the cars come to the ground? 12 ft

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? 12ft

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?

Answer 1

Given, radius of the Ferris wheel is 106 feet and from the platform, the cars then travel a total of 224 feet in the air.

1) Diameter of the Ferris wheel is = 2*106 feet = 212 feet.

2) The bottom of the cars come to the ground (224-212) feet ,i.e., 12 feet close.

3) The platform if i walk from the platform into the floor of the gondolas with no gap in height is 12 feet high.

4) The center of the Ferris wheel from the ground is (106+12) feet ,i.e., 118 feet high.

5) The coordinates of the center of the Ferris wheel will be (0,118).

6) Here, the radius of the Ferris wheel is 106 feet and the coordinates of center is (0,118).

Ferris wheel represent a circle here.

The general equation of a circle is : (x-a)²+(y-b)²=r², where (a,b) is the center and r is the radius.

Putting a = 0, b = 118, r = 106 we get, (x-0)²+(y-118)² = 106² ,i.e., x²+(y-118)² = 106².

7) The circumference of Ferris wheel is = [2*(22/7)*106] feet = 4664/7 feet

Therefore, In one rotation, a patron travels 4664/7 feet while riding the Ferris wheel at the State Fair of Texas.