The Exciting World of Windmill Blades

Question: How can we create a sine model for the height of the end of windmill blade based on its rotation speed and length?

Answer:

To create a sine model for the height of the end of a windmill blade, we need to consider the length of the blade, the vertical shift (height of the windmill), and the rotation speed. In this case, the windmill blades are 15 feet long, rotate 3 times per minute, with the axis at 40 feet from the ground.

In this scenario, the length of the blade, a, is 15 feet and the vertical shift, k, is 40 feet. The period of rotation is 20 seconds, calculated as 60 seconds (1 minute) divided by the number of rotations per minute (3). To determine the coefficient b, we use the formula b = π/period. Therefore, b = π/10.

Based on the given data, the sine model for the height of the end of one blade as a function of time t (in seconds) can be expressed as:

y = 15sin(π/10t) + 40

Therefore, the correct sine model for this windmill scenario is option C.