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

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.\na is the\nthe ver\nlength of the blade\na =\nheight of the windmill\nnumber of rotations per minute\ndone

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.\na is the\nthe ver\nlength of the blade\na =\nheight of the windmill\nnumber of rotations per minute\ndone

Answer

Answer:

a is the length of the blade; a = 15

Explanation:

Step1: Analyze the sine - model components

The general form of the sine - model is $y=a\sin(bt)+k$. In the context of the height of the end of a wind - mill blade, $k$ represents the vertical shift (height of the axis of rotation from the ground), $a$ represents the amplitude, $b$ is related to the period, and $t$ is time.

Step2: Determine the value of a

The amplitude $a$ of the sine function for the height of the end of the blade is equal to the length of the blade. Since the blade is 15 feet long, $a = 15$. The height of the windmill (axis height) is related to $k$ (in this case $k = 40$), and the number of rotations per minute is used to find $b$.