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A sinusoidal equation can be used to model the height of the
waterwheel above the water.
Response:
Diameter of the wheel = 40 feet
Point P is a point on an axis parallel to the water surface on the circumference of the wheel.
The time it takes point to reach maximum height = 2 seconds
Location of the center of the water wheel = 15 feet above the center of the water and 15 feet to the right of the mill.
Required:
The model of the distance of the point P from the surface of the water.
Solution:
The distance of the point p above the water surface vary sinusoidally,
according to the following equation;
h = A·sin(ω·t + ∅)) + k
The time it takes the wheel to complete a cycle, T = 4 × 2 s = 8 s
[tex]T = \mathbf{\dfrac{2 \cdot \pi}{\omega}}[/tex]
Therefore;
[tex]\omega = \dfrac{2 \cdot \pi}{8} = \dfrac{\pi}{4}[/tex]
A = The amplitude = The radius of the wheel = [tex]\frac{40 \, ft.}{2}[/tex] = 20 ft.
The vertical shift, k = 15
The horizontal shift is given by the equation;
At t = 0, sin(ω×0 + ∅) = 0
sin(∅) = 0
∅ = 0
The sinusoidal equation that models the distance d is therefore;
Please find attached the drawing of the situation and graph of the
sinusoidal equation.
Learn more about sinusoidal equations here:
https://brainly.com/question/12078395
