The blades of a windmill turn on an axis that is 40 feet from the ground. the blades are 15 feet long and complete 3 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.

a is the
the vertical shift, k, is the
a =
k =

a is the _amplitude_(Length of the blades)_

The vertical shift, k, is the _Mill shaft height_

Step-by-step explanation:

In this problem the amplitude of the sinusoidal function is given by the length of the blades.

The mill is 40 feet above the ground, therefore the function must be displaced 40 units up on the y axis. So:

We know that the blades have an angular velocity w = 3 rotations per minute.

One rotation =

1 minute = 60 sec.

So:

Finally:

a is the _amplitude_(Length of the blades)_

The vertical shift, k, is the _Mill shaft height_

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step-by-step explanation:

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