Q.50 - Precalculus Enhanced with Graphing Utilities

Question

Ferris Wheel In 2008, the Singapore Flyer opened as the world’s largest Ferris wheel. It has a maximum height of 165 meters and a diameter of 150 meters, with one full

rotation taking approximately 30 minutes. Find an equation for the wheel if the center of the wheel is on the y-axis.

Step-by-Step Solution

Answer

An equation for the wheel if the center of the wheel is on the y-axis is $x^2+{(y-90)}^2={75}^2.$

Step 1.Given information

Here a wheel diameter of 150cm with a maximum height of 165 cm 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 of the wheel

According to the given statement diameter of the wheel is 150 cm, the radius will be 75cm. Here maximum height is 165cm., so the height of the wheelbase is$165cm-150cm=15cm$. hence the center of the given wheel is $$\begin{gathered} center=(0,15+radius), here center is on y axis \\ =(0,15+75) \\ =(0,90) \end{gathered}$$

Step 3. Finding the equation of the wheel

In this  the equation of the wheel  is the equal  equation of a circle,  then  the radius is 75cm and center is (0,90), thus  the equation of the wheel  is $$\begin{gathered} {(x-0)}^2+{(y-90)}^2={75}^2 , \sin ce equation of a circle is {(x-h)}^2+{(y-k)}^2=r^2 \\ x^2+{(y-90)}^2={75}^2. \end{gathered}$$