The sine model for the height (in feet) of the end of one windmill blade as a function of time t (in seconds) y = 30sin(π/15t)+30.
<h3>What is sine function with time?</h3>
The period of a sine function is equal to the 2π and it repeats after each 2π units.
The sine model can be given as,
![y = a\sin(bt) +k](https://tex.z-dn.net/?f=y%20%3D%20a%5Csin%28bt%29%20%2Bk)
The blades are 10 feet long and complete 2 rotations every minute. Thus the period is,
![b=\dfrac{2\pi}{60}\times2\\b=\dfrac{\pi}{15}\\](https://tex.z-dn.net/?f=b%3D%5Cdfrac%7B2%5Cpi%7D%7B60%7D%5Ctimes2%5C%5Cb%3D%5Cdfrac%7B%5Cpi%7D%7B15%7D%5C%5C)
The blades of a windmill turn on an axis that is 30 feet from the ground. Thus,
![k=30](https://tex.z-dn.net/?f=k%3D30)
The blades are 10 feet long. Thus,
![a=10](https://tex.z-dn.net/?f=a%3D10)
Put these values in the above formula as,
![y = 30\sin(\dfrac{\pi}{15}t) +30](https://tex.z-dn.net/?f=y%20%3D%2030%5Csin%28%5Cdfrac%7B%5Cpi%7D%7B15%7Dt%29%20%2B30)
Thus, the sine model for the height (in feet) of the end of one windmill blade as a function of time t (in seconds) y = 30sin(π/15t)+30.
Learn more about the sine function with time here;
brainly.com/question/1542636