SOLUTION: The blade on a windmill takes 8 seconds to make a full rotation. At its lowest point, the end of a blade is 0.5 m from the ground; at its highest point, the end of the blade is 6.5

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Question 1111960: The blade on a windmill takes 8 seconds to make a full rotation. At its lowest point, the end of a blade is 0.5 m from the ground; at its highest point, the end of the blade is 6.5 m from the ground.
a. Start the end of the blade at its highest point and graph the path of the blade over a period of 24 seconds
b. Determine the function that models the point at the end of the blade
c. Predict the height of the endpoint after 135 seconds
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Since we are starting at its highest point, we can use a cosine function with no horizontal shift.

The maximum value is 6.5; the minimum is 0.5. That means an amplitude of 3 and a center line of 3.5.

The equation is then
3cos%28kx%29%2B3.5
where the horizontal compression factor k is 2pi divided by the period. Since the period of the windmill's rotation is 8 seconds, the equation is
3cos%28%282pi%2F8%29x%29%2B3.5

Here is a graph of 4 periods, including the specified interval from 0 to 24 seconds:

graph%28400%2C200%2C-4%2C28%2C-2%2C8%2C3cos%28%282pi%2F8%29x%29%2B3.5%29

Since the period is 8 seconds, the height at 135 seconds will be the same as the height at 7 seconds:
3cos%2814pi%2F8%29%2B3.5+=+5.62132