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Tyrant4life
28.05.2021 •
Mathematics
The Great Laxey Wheel, located on the Isle of Man, is the largest working water wheel in the world. The highest point of a bucket on the wheel is 70.5 feet above the viewing platform, and the lowest point is 2 feet below the viewing platform. The wheel makes a complete turn every 24 seconds. Write a model for the height h (in feet) of the bucket as a function of time t (in seconds) given that the bucket is at its lowest point when t
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Ответ:
h(t)=-36.25cos(0.2618t)+34.25
Step-by-step explanation:
We can start by drawing a sketch of what the whaterwheel's height over time looks like. (See attached picture.)
We can see on the graph that at t=0, the bucket will be located at its lowest point. So in this case we can make use of a cosine function. Cosine functions look like this:
where:
A=amplitude
b= vertical shift.
So let's find each of the necessary data:
The amplitude is the distance between the highest point of the trajectory and the middle point of the sine wave, so:
A=36.25 ft
since the trajectory starts at its lowest point when t=0 we will make the amplitude a negative amplitude, so:
A=-36.25ft
Next, we can find the angular speed:
Where T is the period (the time it takes the wheel to make one whole turn) so:
the phase shift in this case is zero since the graph starts at the lowest point.
the vertical shift is the distance between the x-axis and the middle point of the graph. So we find the midpoint between the lowest and the highest point of the graph:
b=34.25ft
so we can now input all this data into the formula to get:
Ответ: