a.
To create a model for h .
The equation for the model is
Given:
Given, Jacob and Emily ride a Ferris wheel at a carnival in Billings, Montana. The wheel has a 16-m diameter and turns at 3rpm with its lowest point 1 m above the ground. Assume that Jacob and Emily’s height h above the ground is a sinusoidal function of time t (in seconds), where
Calculation:
Since at
The diameter of the wheel is 16 m. So, the height of the rider changes from 8 feet below to 8 feet above the center i.e., -8 to 8. Hence the amplitude of the motion is 8.
Hence,
k is the vertical shift of the motion above the ground.
Here the shift of center of wheel above the ground is 1+8=9 m.
Hence,
Given the wheel completes 3 rotations in 1 minute i.e., 60 seconds. Hence, each rotation takes 60/3=20 seconds. So, the period is 20 seconds.
The frequency is given by:
Hence, the equation for the model is
Conclusion:
The equation for the model is
b.
To draw a graph of h for
The graph of h for
Given:
Given, Jacob and Emily ride a Ferris wheel at a carnival in Billings, Montana. The wheel has a 16-m diameter and turns at 3rpm with its lowest point 1 m above the ground. Assume that Jacob and Emily’s height h above the ground is a sinusoidal function of time t (in seconds), where
Calculation:
Graphing the equation using a graphing utility for
Conclusion:
The graph of h for
c.
To estimate the height of Jacob and Emily above the ground at
The height of Jacob and Emily above the ground at
Given:
Given, Jacob and Emily ride a Ferris wheel at a carnival in Billings, Montana. The wheel has a 16-m diameter and turns at 3rpm with its lowest point 1 m above the ground. Assume that Jacob and Emily’s height h above the ground is a sinusoidal function of time t (in seconds), where
Calculation:
The equation of the motion is
When
When
Hence, the height of Jacob and Emily above the ground at
Conclusion:
The height of Jacob and Emily above the ground at
Chapter 4 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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