Activity: The Ferris Wheel
Rotation
Objective: Model the height of a
rider on a Ferris wheel over time.
Phase 1: The Scenario (Predict) Imagine you board the "London Eye Flyer," a Ferris wheel with the following
specifications:
●​ Diameter: 40 meters (Radius = 20m)
●​ Platform Height: 2 meters above the ground (this is where you get on).
●​ Rotation Speed: It takes 20 minutes to complete one full revolution.
Task 1: (Pair Task)How would you describe the height of a rider on a ferris wheel on y-axis with time on x-axis.
Discussion Points:
●​ The Central axis of rotation's height can be taken as the x-axis.
Phase 2: (The Data) The ride is periodic, meaning it repeats its "story" over and over. Let’s map out the first
chapter of that story. Using the details above, Complete the table of values representing their height at specific
time intervals:
Time (minutes)
Position on the wheel
0
Bottom (Start)
Height (in m)
5
10
Top
15
20
Bottom (End)
Calculations:
Midline (d): What is the average height?
Calculation:
Reach (Maximum) Amplitude (a): How far do you
go above or below the center?
Calculation:
Speed (Period) (b): How long is one cycle?
Calculation:
Improve your graph using the data you calculated.
Reflect & Learn:
If the ride lasted 40 minutes, what would the height be after 40 minutes?
What about 60 minutes?
This "reset" time is what we call the Period.
◦
Calculate the Speed Factor (b): A full circle is 360 or 2 π radians. If it takes you 20 minutes to cover that
distance, your "speed" is:
Phase 4: Building the "Safety Model" (The Equation) [Discuss with the teacher]
In mathematics, we use a special "code" to describe these smooth, repeating waves.
h(t) = ( Reach)( Periodic WaveType )(Speed x time ) + Midline
Key points
Explanation
Remarks/Notes
Domain ( time)
Range ( Heights)
Periodicity
Central Height (axis of rotation)
How did we come up with sine or cosine functions?
Phase 5: The Investigation Challenge : The "Emergency Stop":
The ride operator hits the emergency stop at t = 7minutes.
1.​ Look at your graph: Are you above or below the center of the wheel?
2.​ Use your equation: Calculate your exact height at 7 minutes.
For Teachers:
Lesson -1 (Desmos)
Lesson -2 (Desmos) Slide 27 has a Ferris wheel animation..
Extension (From Gemini):
Problem 2: The Heartbeat Monitor (Medicine)
A patient is hooked up to an EKG monitor. We are tracking the pressure of the blood against the artery walls as
the heart pumps.
●​ The Data: The patient’s blood pressure fluctuates between a minimum (diastolic) of 80 mmHg and a
maximum (systolic) of 120 mmHg.
●​ The Cycle: The patient’s heart beats 60 times per minute (which means 1 beat every 1 second).
Inquiry Questions:
1.​ The Period: If the heart beats once per second, what is the "Period" of this wave?
2.​ The Shift: Unlike the Ferris wheel, we start our measurement right as the heart pulses at its maximum
pressure (120 mmHg). Which trigonometric function starts at the maximum?
3.​ The Challenge: If the patient starts exercising and their heart rate doubles, how would that change the
shape of the graph? Would it get taller (Amplitude) or "squished" (Period)?
Problem 3: The Tidal Mystery (Marine Biology)
In the Bay of Fundy, the water level changes dramatically as the moon’s gravity "pulls" the ocean back and forth.
You are a marine biologist tracking the water depth at a specific pier.
●​ The Data: At Low Tide (6:00 AM), the water is only 2 meters deep. At High Tide (12:00 PM), the water
reaches a depth of 14 meters.
●​ The Cycle: The tide goes from low to high and back to low every 12 hours.
Inquiry Questions:
1.​ The Midline: What is the "average" depth of the water?
2.​ The Amplitude: How much does the moon "pull" the water above and below that average?
3.​ The Model: If t=0 is Low Tide (the bottom), which (Sine, Cosine, or Reflected Cosine) will you use to
write the equation
Resources & References: Ideas, Thoughts and strategies by: Author. Gemini was used to rephrase to make students friendly and avoid grammar mistakes.