Graphing the movement of the Falkirk wheel with a sine curve?

[greyskies12]

The Falkirk wheel is this: http://www.youtube.com/watch?v=n61KUGDWz2A. The information we're given: at 4:22.43 PM, the wheel is upright. At 4:25.58 it's completely horizontal. At 4:28.29 PM it's upright again. The wheel is 115 ft or 25 meters tall. How do I model the movement of this with the sine model f(x)=a sin(b(x+c))+d? Thank you! Cosine works as well. this problem is killing me.

I'm fairly sure the amplitude (a) is 57.5? and the vertical shift (d) is also 57.5? Is that true? How do I find the rest?

 

[greyskies12]

Correction: the wheel is 35 meters tall. NOT 25.

 

[wjm11]

The Falkirk wheel is this: http://www.youtube.com/watch?v=n61KUGDWz2A. The information we're given: at 4:22.43 PM, the wheel is upright. At 4:25.58 it's completely horizontal. At 4:28.29 PM it's upright again. The wheel is 115 ft or 25 meters tall. How do I model the movement of this with the sine model f(x)=a sin(b(x+c))+d? Thank you! Cosine works as well. this problem is killing me.

I'm fairly sure the amplitude (a) is 57.5? and the vertical shift (d) is also 57.5? Is that true? How do I find the rest?

The vertical shift is whatever the center of rotation is above water level. Your period is the time difference between the two "upright" positions. You might want to convert your times into seconds. I suggest using cosine rather than sine, since you have info on the "upright" position. Cosine starts at peak value at t=0 before the phase shift is applied. Use the first given upright time to find your phase shift.

Just Google something like "ferris wheel sinusoid problem" and you should find many examples, including several on youtube.

 

[DrPhil]

The Falkirk wheel is this: http://www.youtube.com/watch?v=n61KUGDWz2A. The information we're given: at 4:22.43 PM, the wheel is upright. At 4:25.58 it's completely horizontal. At 4:28.29 PM it's upright again. The wheel is 115 ft or 25 meters tall. How do I model the movement of this with the sine model f(x)=a sin(b(x+c))+d? Thank you! Cosine works as well. this problem is killing me.

I'm fairly sure the amplitude (a) is 57.5? and the vertical shift (d) is also 57.5? Is that true? How do I find the rest?

The two "upright" times should tell you the half-period. The boat (or the center of the circle containing the boat?) moves from (d-a) to (d+a). Unfortunately the "horizontal" time is NOT halfway between the other two times, so the motion is NOT sinusoidal. Best you can do is ignore the horizontal time, and calculate b so that b times the time difference is pi. Then choose the phase c such that the sine (or cosine) has the value -1 when x=0.

The wheel is fascinating, but the given information seems a bit shaky. What measurement on the wheel corresponds to "tall"? What is the time, really? When presented with incomplete or contradictory information, specify what it is you don't know and what assumptions you are making - then proceed as if you really know what you are doing.

 

[wjm11]

The two "upright" times should tell you the half-period. The boat (or the center of the circle containing the boat?) moves from (d-a) to (d+a). Unfortunately the "horizontal" time is NOT halfway between the other two times, so the motion is NOT sinusoidal. Best you can do is ignore the horizontal time, and calculate b so that b times the time difference is pi. Then choose the phase c such that the sine (or cosine) has the value -1 when x=0.

The wheel is fascinating, but the given information seems a bit shaky. What measurement on the wheel corresponds to "tall"? What is the time, really? When presented with incomplete or contradictory information, specify what it is you don't know and what assumptions you are making - then proceed as if you really know what you are doing.

Dr. Phil is correct regarding the two "upright" times as being the half-period. I probably misinterpreted your meaning when you said upright. I took it to mean one complete rotation. You probably only meant one-half rotation.