Domain and Range of a Ferris Wheel: Explanation and Solution

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In summary, the question is asking for the domain and range of a function that relates the elevation of a point on a Ferris wheel to time. The radius of the Ferris wheel is 7m and the highest point is 15.5m off the ground. It takes 45 seconds to complete one revolution. The domain is D:{0<=t<=45}s and the range is R:{1.5<=h<=15.5}. The answer key may be incorrect as it states the range as R:{1.5<=h<=17.5}.
  • #1
Veronica_Oles
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Homework Statement


Ferris wheel has radius of 7m and its highest point is 15.5 m off the ground. It takes 45 seconds to complete one revolution. State the domain and range.

Homework Equations

The Attempt at a Solution


I know that the domain is D:{0<=t<=45}s
But for the range I thought the range was R:{1.5<=h<=15.5} but in the answer key it says range is R:{1.5<=h<=17.5} and I'm having troubling understanding why it's 17.5? Can someone help me figure it out.
 
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  • #2
Veronica_Oles said:

Homework Statement


Ferris wheel has radius of 7m and its highest point is 15.5 m off the ground. It takes 45 seconds to complete one revolution. State the domain and range.

Homework Equations

The Attempt at a Solution


I know that the domain is D:{0<=t<=45}s
But for the range I thought the range was R:{1.5<=h<=15.5} but in the answer key it says range is R:{1.5<=h<=17.5} and I'm having troubling understanding why it's 17.5? Can someone help me figure it out.
What is the function ?
 
  • #3
SammyS said:
What is the function ?
That is not provided in the question, unless I have to find it?
 
  • #4
Veronica_Oles said:
That is not provided in the question, unless I have to find it?
What is it in words ?
 
  • #5
SammyS said:
What is it in words ?
Is not the question?
 
  • #6
I can guess that you are referring to the domain and range of the function which relates the elevation of some point on the Farris Wheel to time. But it's just a guess on my part.

If this is the case, then you are referring to the elevation of said point as a function of time, as the Farris Wheel rotates.
 
  • #7
Veronica_Oles said:

Homework Statement


Ferris wheel has radius of 7m and its highest point is 15.5 m off the ground. It takes 45 seconds to complete one revolution. State the domain and range.

Homework Equations

The Attempt at a Solution


I know that the domain is D:{0<=t<=45}s
But for the range I thought the range was R:{1.5<=h<=15.5} but in the answer key it says range is R:{1.5<=h<=17.5} and I'm having troubling understanding why it's 17.5? Can someone help me figure it out.

If you stated the question correctly, then your answer is right and the answer key is wrong.
 
  • #8
Ray Vickson said:
If you stated the question correctly, then your answer is right and the answer key is wrong.
That's what I was thinking. Thanks though.
 

FAQ: Domain and Range of a Ferris Wheel: Explanation and Solution

1. What is the domain of a ferris wheel?

The domain of a ferris wheel is the set of all possible inputs or independent variables, typically represented by the angle or time. In the context of a ferris wheel, the domain would represent the rotation or position of the wheel.

2. What is the range of a ferris wheel?

The range of a ferris wheel is the set of all possible outputs or dependent variables, typically represented by the height or distance. In the context of a ferris wheel, the range would represent the height or distance from the ground at a given angle or time.

3. How is the domain and range of a ferris wheel related?

The domain and range of a ferris wheel are related through the motion of the wheel. As the wheel rotates, the angle or time (domain) changes, resulting in a change in the height or distance (range). The two are dependent on each other.

4. How can we determine the domain and range of a ferris wheel?

To determine the domain and range of a ferris wheel, we can use the equation for the height of a point on a circle, which is h = rcosθ, where r is the radius of the wheel and θ is the angle or time. This equation can be used to calculate the height at any given angle or time, thus determining the range. The domain can be determined by identifying the possible values for θ based on the rotation of the wheel.

5. Can the domain and range of a ferris wheel be infinite?

Yes, the domain and range of a ferris wheel can be infinite. This is because the wheel can continue to rotate indefinitely, resulting in an infinite number of possible angles or times and corresponding heights or distances. However, in practical applications, the domain and range may be limited by factors such as the size of the wheel or the duration of the ride.

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