Sinusoidal Function Applications 1. Ferris Wheel Problem As you ride the Ferris wheel, your distance from the ground varies sinusoidally with time. When the last seat1 is filled and the Ferris wheel starts, your seat is at the position shown in the figure below. Let t be the number of seconds that have elapsed since the Ferris wheel started. You find that it takes you 3 seconds to reach the top, 43 feet above ground, and that the wheel makes a revolution once every 24 seconds. The diameter of the wheel is 40 feet. a. Sketch a graph of this sinusoidal function. b. What is the lowest you go as the Ferris wheel turns? Seat Rotation c. Find an equation of this sinusoid. d. Predict your height above ground when you have been riding for 4 seconds.
Sinusoidal Function Applications 1. Ferris Wheel Problem As you ride the Ferris wheel, your distance from the ground varies sinusoidally with time. When the last seat1 is filled and the Ferris wheel starts, your seat is at the position shown in the figure below. Let t be the number of seconds that have elapsed since the Ferris wheel started. You find that it takes you 3 seconds to reach the top, 43 feet above ground, and that the wheel makes a revolution once every 24 seconds. The diameter of the wheel is 40 feet. a. Sketch a graph of this sinusoidal function. b. What is the lowest you go as the Ferris wheel turns? Seat Rotation c. Find an equation of this sinusoid. d. Predict your height above ground when you have been riding for 4 seconds.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Sinusoidal Function Applications**
**1. Ferris Wheel Problem**
As you ride the Ferris wheel, your distance from the ground varies sinusoidally with time. When the last seat is filled and the Ferris wheel starts, your seat is at the position shown in the figure below. Let \( t \) be the number of seconds that have elapsed since the Ferris wheel started. You find that it takes you 3 seconds to reach the top, 43 feet above the ground, and that the wheel makes a revolution once every 24 seconds. The diameter of the wheel is 40 feet.
**Questions:**
a. Sketch a graph of this sinusoidal function.
b. What is the lowest you go as the Ferris wheel turns?
c. Find an equation of this sinusoid.
d. Predict your height above the ground when you have been riding for \( 4 \frac{1}{3} \) seconds.
e. Using Desmos, find the first three times you are 18 feet above ground.
**Explanation of the Diagram:**
The diagram depicts a Ferris wheel with a labeled seat at the top. The diagram shows the Ferris wheel's rotation direction and highlights the seat's distance from the ground (represented by \( d \)).
**Key Points from the Diagram:**
- The Ferris wheel has a diameter of 40 feet, so its radius is 20 feet.
- The Ferris wheel completes one full revolution every 24 seconds.
- The maximum height above the ground is 43 feet.
These details will assist in answering the above questions and help you understand how to model the Ferris wheel's motion using a sinusoidal function.
For a detailed step-by-step solution to each question, please visit our educational resources or use the provided tools like Desmos to visualize and solve the problems interactively.
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