A Web Sketchpad activity helps students make sense of relationships between quantities, in this case the way that the distance a car travels around a Ferris wheel covaries with its height. For a full description of how this resource can be used with students, please read " Investigating Functions with a Ferris Wheel " from the December issue of Mathematics Teacher.
The activity links an animation of a turning Ferris wheel to dynamic graphs relating the quantities of height and distance. When students press the Animate Point button, the car represented by the red dot moves in a counterclockwise direction around the Ferris wheel.
To vary the rate at which the car moves, students can click and drag the car to control the motion. In addition, students can speed up or slow down the animation. By design, the dynamic graph represents only one revolution of the Ferris wheel so that students do not also have to keep track of the number of revolutions of the wheel. On page 2 of the sketch, height is represented on the horizontal axis and distance on the vertical axis. By varying which quantities each axis represents, a teacher can provide additional opportunities for student exploration.
Join Now. View Cart. NCTM Store. Toggle navigation MENU. Log In Not a member? Investigating Functions with a Ferris Wheel: Distance vs. Height Grade: A Web Sketchpad activity helps students make sense of relationships between quantities, in this case the way that the distance a car travels around a Ferris wheel covaries with its height. Instructions For a full description of how this resource can be used with students, please read " Investigating Functions with a Ferris Wheel " from the December issue of Mathematics Teacher.To open this class, I want to get students thinking about the functions they already know, so I post these four questions on the board:.
I prompt students to discuss each of these questions at their tables see slide 2 in ferris wheel ride. I have purposefully left the first two questions open-ended enough that there's no presciption as to whether they should be answered with an equation or graphical representation.
As a I circulate through the room, I listen to the conversations of my students. Also along these lines, I am asking myself:. How many of my students notice that the third question refers to the "equation of a circle," but doesn't call it a function? Concluding this segment of the lesson with a brief whole-class discussion, I ask students to tell me what they know about each of these questions.
As we move on to discussing some of the parameters of a trigonometric function, we'll be able to refer back to these sketches as we try to make use of the structures that different functions share MP7. The notes for today's lesson come in the form of a Problem Solving Task that students will complete in pairs. The Task : Each pair of students gets a sheet of ledger paper 11x17 and I tell them that I'm going to give them a series of prompts to complete.
The next task is to make a table of values - that other great function representation - that lists the height of a rider off the ground at each minute of their ride. I have given a minimal amount of time on each prompt up to this point, and I post this task when I see that the first few groups are ready for it. Some groups will still be finishing up their sketchs and their labeling, and it's fine for them to see where they're going next. One neat benefit of ledger paper is that there's room for two students to write at once - so if one student is still labeling the sketch on the left side of the paper, another can draw this chart.
This is where things really get interesting: I give students minutes to discuss this task and to begin to fill in the chart. As I walk around, I watch to see what they're writing, but I make no comments. I'm watching to see the order in which students fill in the table. Are they going row by row? Are they filling in 0 and 8 first, then the middle?
The latter scenario of starting with the "easy" points reflects a strong understanding of the model, and indeed, this is what I see most students doing. The majority of students will fill in 0, 4 and 8 minutes first because they recognize these as the bottoms and tops of the ride.Back to Course Index.
A New Kind of Graph: The Ferris Wheel Ride
Home Trigonometry Applications of Trigonometry Functions. Still Confused? Nope, got it. Play next lesson. That's the last lesson Go to next topic. Still don't get it? Play next lesson Practice this topic. Start now and get better math marks! Lesson: 1. Intro Learn Practice. Do better in math today Get Started Now.
Ferris wheel trig problems 2. Tides and water depth trig problems 3. Spring simple harmonic motion trig problems Back to Course Index. Don't just watch, practice makes perfect. A Ferris wheel has a radius of 18 meters and a center C which is 20m above the ground. It rotates once every 32 seconds in the direction shown in the diagram. A platform allows a passenger to get on the Ferris wheel at a point P which is 20m above the ground. Graph how the height h of a passenger varies with respect to the elapsed time t during one rotation of the Ferris wheel.
Clearly show at least 5 points on the graph. Determine a sinusoidal function that gives the passenger's height, h, in meters, above the ground as a function of time t seconds.Notice how the purple point indicates a height of feet. Use the trigonometric function that appears on the right to solve for the shortest time it takes for any rider to reach this height of feet.
Type your answer here…. Slide the purple slider entitled "Other Solutions? Then, algebraically determine the next few times for which this occurs.Sinusoidal ferris wheel problem
Confirm that your results match with the appropriate coordinates of the other purple points. News Feed. App Downloads. Ferris Wheel 2 : Modeling with Trigonometric Functions. Author: Tim Brzezinski. This applet graphs the height of an person riding a Ferris Wheel vs. There are several parameters you can adjust here: Period Number of Revs to Complete Height of Lowest Car Diameter of Wheel You can also manually enter y -coordinate of the purple point. You can also move this point if you choose.
Interact with this applet for a few minutes. Then answer the questions that follow. Hit the refresh recycle button to reset it. Then slide the black slider all the way to the right.I tried something new today. Desmos is a staple resource in my class, but this week I tried giving a Desmos activity for homework. I have been rethinking the purpose and efficacy of homework over the course of this year.
This is how my Desmos homework went. Students started engaging in the task by noticing and wondering in Act 1. We focused on the first two questions.
Chair Height on a Ferris Wheel
Students used properties of isosceles right triangles, pythagorean theorem and also trig functions to solve for the height of each position on the ferris wheel. All methods were displayed and we discussed the benefits and limits of each method. These were some of the responses:. We quickly looked at a graph of a sine function and talked about how this function produced all of our data points.
Ferris Wheel for Graphing Trig Functions
The goal of this homework assignment was for them to practice using trig functions in geometry while also stepping into the idea of graphing trig functions using only what they know about trig functions in geometry and graphing data.
Students were given the chance tonight to go back into Desmos and revise their graph if they think it was needed. In your class: What is the purpose of homework in one sentence or less? You are commenting using your WordPress. You are commenting using your Google account. You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email.
The wheel rotates once every three minutes. Answer to the nearest tenth. Your solution is on the right track. The question asks you to use time in minutes, so you should not convert to seconds. This is a straightforward question and I strongly suggest that you go over your textbook or at least one of these following resources:.
Because you did not attempt to solve the problem yourself, I will not provide a detailed solution. If you run into trouble trying to complete the problem yourself, let me know in a comment and I may be able to help.
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Desmos for Homework
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Join me on Patreon and help support this website. The Ferris wheel consists of an upright wheel with passenger gondolas seats attached to the rim. These gondolas can freely pivot at the support where they are connected to the Ferris wheel. As a result, the gondolas always hang downwards at all times as the Ferris wheel spins.
To analyze the Ferris wheel physics, we must first simplify the problem. The figure below shows a schematic of the Ferris wheel, illustrating the essentials of the problem. We wish to analyze the forces acting on the passengers at locations 1 and 2. The figure below shows a free-body diagram for the passengers at these locations. Where: mg is the force of gravity pulling down on the passengers, where m is the mass of the passengers and g is the acceleration due to gravity, which is 9.
This acceleration is always pointing towards the center of the wheel. So at location 1 this acceleration is pointing directly down, and at location 2 this acceleration is pointing directly up.
The centripetal acceleration is given by The centripetal acceleration always points towards the center of the circle. So at the bottom of the circle, a P is pointing up. At the top of the circle a P is pointing down.
At these two positions a P is a vector which is aligned parallel with gravity, so their contributions can be directly added together. To solve for N 1 and N 2 we must apply this equation in the vertical direction. The acceleration of the passengers at point C is equal to the acceleration of the Ferris wheel at point P.
This is because point C does not move relative to point P. Therefore, the velocity and acceleration of these two points are the same. This means that the passengers feel "heaviest" at the bottom of the Ferris wheel, and the "lightest" at the top. So basically, the motion of a Ferris wheel affects your bodies "apparent" weight, which varies depending on where you are on the ride.
The riders only feel their "true weight", when the centripetal acceleration is pointing horizontally and has no vector component parallel with gravity, and as a result it has no contribution in the vertical direction. This occurs when the riders are exactly halfway between the top and bottom i.
It's informative to look at an example to get an idea of how much force acts on the passengers. Let's say we have a Ferris wheel with a radius of 50 meters, which makes two full revolutions per minute. At the bottom of the Ferris wheel the passengers experience 1. Now that we understand the physics of a Ferris wheel, one can imagine how important it is for a large radius Ferris wheel to turn slowly, given how much influence the rotation rate w will have on the centripetal acceleration a Pand on N 1 and N 2as a result.
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