Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Find Equation for the Ferris Wheel

In 2008, the Singapore Flyer opened up 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 about 30 minutes. Find an equation for the wheel if the center of the wheel is on the y-axis also known as the x = 0 line.

Let's see what I can do here.

If x = o, then the center is (0, y) = (h, k).

The height of the wheel is 165 meters which is the diameter.

I say the value of y is halfway up the wheel.

So, y = 165/2 = 82.5 meters.

This leads to the center point being (0, 82.5).

The radius is r.

r = (1/2)(150) = 75 meters.

I now have the radius and center point.

I think the next step is to plug this information into the standard form of an equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

Is this correct so far?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Find Equation for the Ferris Wheel

You haven't allowed for any clearance at the bottom with the ground.

The maximum height is 165; subtract the diameter and the lowest point must be 15m off the ground.

So the centre is at 15 + 75 up the y axis.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Equation for the Ferris Wheel

You haven't allowed for any clearance at the bottom with the ground.

The maximum height is 165; subtract the diameter and the lowest point must be 15m off the ground.

So the centre is at 15 + 75 up the y axis.

Bob

So the center is located at (0, 90).

r = 75

(x - h)^2 + (y - k)^2 = r^2

(x - 0)^2 + (y - 90)^2 = (75)^2

x^2 + (y - 90)^2 = 5625

Yes?

Last edited by mathxyz (2024-03-02 18:19:34)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Find Equation for the Ferris Wheel

Yes! 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Find Equation for the Ferris Wheel

Yes! 

Bob

Good. This is a tough application.  To go through it slowly and carefully reaching the right answer is a satisfying feeling of accomplishment.