The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 rotations every minute.

Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t=0 and that the windmill turns counterclockwise at a constant rate.

The sine model is y=10 sin(1/30 t) + 30. The 30 represents default distance from the ground, and the ten is required to represent the length of the blades. Every 30 seconds, one rotation completes, so t must be multiplied by 1/30.

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AFOKE88 AFOKE88 · Answer 2 · 2022-05-11T05:26:58-04:00

The sine model for the height (in feet) of the end of one windmill blade as a function of time t (in seconds) is; y = 30sin(πt/15) + 30

How to solve Sine Functions?

The period of a sine function is represnted as;

b = 2π

This period is usually repeated after each 2π units.

The sine model is expressed as;

y = a(sin (bt)) + k

We are told that the blades are 10 feet long and complete 2 rotations every minute. Thus the period is;

b = (2π/60) * 2

b = π/15

The blades of a windmill turn on an axis that is 30 feet from the ground and the blades are 10 ft long. Thus,

k = 30 and a = 10

Plugging the relevant values into the given formula gives;

y = 30sin(πt/15) + 30

Thus, the sine model for the height (in feet) of the end of one windmill blade as a function of time t (in seconds) is;

y = 30sin(πt/15) + 30

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