Question

A Ferris wheel is 28 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 16 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn. a. Find the amplitude, midline, and period of h(t). Enter the exact answers. Amplitude: A= meters Midline: h= meters Period: P= minutes b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t=0. Find a formula for the height function h(t). Hints: What is the value of h(0)? Is this the maximum value of h(t), the minimum value of h(t), or a value between the two? The function sin(t) has a value between its maximum and minimum at t=0 , so can h(t) be a straight sine function? The function cos(t) has its maximum at t=0, so can h(t) be a straight cosine function? c. If the Ferris wheel continues to turn, how high off the ground is a person after 60 minutes?

          A Ferris wheel is 28 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 16 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn.
a. Find the amplitude, midline, and period of h(t).
Enter the exact answers.
Amplitude: A=  
 meters
Midline: h=  
 meters
Period: P=  
 minutes
b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t=0. Find a formula for the height function h(t).
Hints:
What is the value of h(0)?
Is this the maximum value of h(t), the minimum value of h(t), or a value between the two?
The function sin(t) has a value between its maximum and minimum at t=0 , so can h(t) be a straight sine function?
The function cos(t) has its maximum at t=0, so can h(t) be a straight cosine function?
c. If the Ferris wheel continues to turn, how high off the ground is a person after 60 minutes?

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Added by Elizabeth P.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Gregory Higby

05/31/2023

Step 1

The midline is the average height, which is 15 meters above the ground. The period is the time it takes for one complete revolution, which is 16 minutes. Show more…

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A Ferris wheel is 28 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 16 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn. a. Find the amplitude, midline, and period of h(t). Enter the exact answers. Amplitude: A= meters Midline: h= meters Period: P= minutes b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t=0. Find a formula for the height function h(t). Hints: What is the value of h(0)? Is this the maximum value of h(t), the minimum value of h(t), or a value between the two? The function sin(t) has a value between its maximum and minimum at t=0 , so can h(t) be a straight sine function? The function cos(t) has its maximum at t=0, so can h(t) be a straight cosine function? c. If the Ferris wheel continues to turn, how high off the ground is a person after 60 minutes?

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Transcript

00:01 There's a lot of words here, but the problem isn't too bad because you're starting on this at one meter off the ground.

00:08 I'm just going to go clockwise this way just to give you the visual.

00:12 And the diameter is 28, which means the radius from the center down would be half of that.

00:22 So the radius would be 14, which means the center of this would be equal to 015.

00:29 I think we can answer the question.

00:30 We just need one more thing, is they tell you you complete one revolution in 16 minutes.

00:36 So that's actually your period.

00:38 So the part a asks you all those questions.

00:41 Find the amplitude, which is actually equal to the radius of 14.

00:46 The midline would be the equation y equals 15.

00:53 It's where the center is located.

00:55 And then the period, which i already wrote down, was 16 minutes in minutes, if you're curious.

01:03 Oh, i guess amplitude is in meters.

01:09 Same with the midline.

01:12 But anyway, we can answer letter b, and they give you a lot of hints.

01:16 But if you just think about what that graph is going to look like, then it looks like this.

01:22 And you started below the midline.

01:25 Midline would be that horizontal line.

01:27 So what that tells me is my equation is going to be a negative cosine.

01:31 I think that's what some of the hints were trying to get you to.

01:34 The amplitude is 14...

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