Math Problem Statement
Snatch a graph for the following problem
Solution
Here is the graph modeling the height of a person on the Ferris wheel over time. The important features are:
- Amplitude (14 feet): The radius of the Ferris wheel, which defines the distance from the center to the highest or lowest point.
- Period (32 seconds): The time for one full revolution.
- Vertical shift (16 feet): The center of the wheel is 16 feet above the ground.
- Maximum height (30 feet): The person reaches this height after 7 seconds.
- Minimum height (2 feet): The lowest point reached by the person.
Let me know if you want further details or have any questions.
Here are some related questions:
- What would happen to the graph if the Ferris wheel's diameter increased?
- How would the graph change if the period was longer?
- What is the height after 10 seconds?
- How would the equation change if the person starts at the top?
- What would be the phase shift if the person reaches the top after 5 seconds?
Tip: In trigonometric modeling, phase shifts help position sinusoidal functions based on specific initial conditions.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Periodic Functions
Amplitude and Period
Vertical Shift
Formulas
y(t) = A * sin(B(t - C)) + D
Amplitude = Radius of Ferris wheel = 14 feet
Period = 32 seconds
Vertical Shift = Diameter/2 + Ground clearance = 16 feet
Maximum height = Vertical shift + Amplitude = 30 feet
Theorems
Sine Wave Equation for Modeling Periodic Motion
Suitable Grade Level
Grades 10-12
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