Question

The blades of a windmill turn on an axis that is 30 feet from the ground. The blades are 10 feet long and complete 2 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.

y = 30 sine (StartFraction pi Over 15 EndFraction t) + 10
y = 30 sine (StartFraction pi Over 15 EndFraction t) + 30
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 10
y = 10 sine (StartFraction pi Over 15 EndFraction t) + 30

Answer 1

Explanation:

The sine model is y=10 sin(1/30 t) + 30. The 30 represents default distance from the ground, and the ten is required to represent the length of the blades. Every 30 seconds, one rotation completes, so t must be multiplied by 1/30.