Q.49 - Precalculus Enhanced with Graphing Utilities

Question

Ferris Wheel The original Ferris wheel was built in 1893 by Pittsburgh, Pennsylvania, bridge builder George W. Ferris.

The Ferris wheel was originally built for the 1893 World’s Fair in Chicago and was later reconstructed for the 1904 World’s Fair in St. Louis. It had a maximum height of

264 feet and a wheel diameter of 250 feet. Find an equation for the wheel if the center of the wheel is on the y-axis.

Step-by-Step Solution

Answer

The equation for the wheel  if the center of the wheel is on the y-axis is

$x^2+{(y-139)}^2={\left(125\right)}^2$ 

Step 1.Given information

In this question, a wheel diameter of 250 feet with a maximum height of 264 feet is given.

 we need to find an equation for the wheel if the center of the wheel is on the y-axis. 

Step 2. Finding the radius and center

Here diameter of the wheel is 250 feet, then radius will be 125ft .

Given maximum height is 264ft., so the height of wheelbase is $264ft-250ft=14ft$

Then  $$\begin{gathered} center =(0,!4+radius) , \sin ce center is on the y axis \\ =(0,14+125) \\ =(0,139) \end{gathered}$$

Step 3. Find the equation of the wheel

Here the equation of the wheel  is the equal  equation of a circle,  then  the radius is 125 ft and center is (0,139)

 then the equation of the wheel  is $$\begin{gathered} {(x-0)}^2+{(y-139)}^2={\left(125\right)}^2 , \sin ce equation of a circle is {(x-h)}^2+{(y-k)}^2=r^2 \\ x^2+{(y-139)}^2={\left(125\right)}^2. \end{gathered}$$