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URGENT!!! A farmer has a small windmill on her farm that is 4 m in diameter and its centre is 17 m above the ground. Before it starts spinning, a lady bug lands on the very bottom edge of the propeller that is pointing downward. Once it starts spinning, it takes only 6 seconds for the ladybug to complete two complete cycles around the windmill.

a) What are the amplitude and axis of the curve going to be for the function that
represents this situation? How do you know?
Hint: How are these two values related to this real-world example?
b) Determine the maximum and minimum height from the ground that the ladybug
will have on the windmill. Explain your reasoning.
c) What is the period of the windmill? Explain your reasoning.

User GCoh
by
8.2k points

1 Answer

2 votes

Answer:

a) The amplitude and axis of the curve can be determined from the given information. In this real-world example, the windmill's propeller rotates in a circular motion. The amplitude of the curve represents the distance from the center of the windmill to the highest or lowest point on the propeller. Since the windmill has a diameter of 4 m, the radius (and therefore the amplitude) is half of that, which is 2 m.

The axis of the curve represents the vertical line passing through the center of the windmill. In this case, the windmill's center is 17 m above the ground. Thus, the axis of the curve is a horizontal line at a height of 17 m.

b) To determine the maximum and minimum height of the ladybug on the windmill, we need to consider the amplitude. Since the amplitude is 2 m, the maximum height the ladybug will reach is 17 m + 2 m = 19 m above the ground. The minimum height will be 17 m - 2 m = 15 m above the ground.

c) The period of the windmill represents the time it takes for the ladybug to complete one full cycle around the windmill. From the given information, we know that the ladybug takes 6 seconds to complete two complete cycles. Therefore, the period of the windmill can be calculated by dividing the total time by the number of cycles, which is 6 seconds / 2 = 3 seconds per cycle.

In summary:

a) The amplitude is 2 m, and the axis is a horizontal line at a height of 17 m.

b) The maximum height of the ladybug is 19 m above the ground, and the minimum height is 15 m above the ground.

c) The period of the windmill is 3 seconds per cycle.

Explanation:

Hope this helps!! <3

User Dmitry Pavlov
by
9.0k points