Question 1199333: A Ferris wheel has a diameter of 20m. The center of the circle is 11m off the ground. The Ferris wheel makes a complete rotation in 30 seconds.
a) Draw the graph of the height of a rider vs time. The graph should have 2 cycles and the graph should start when the rider boards the Ferris wheel. Determine an equation that models the situation.
b) Draw the graph of the height of a rider vs. time. The graph should have 2 cycles and the graph should start when the rider is at the top of the Ferris wheel.
c) Draw the graph of the height of a rider vs. time. The graph should have 2 cycles and the graph should start when the rider is halfway between the highest and lowest point in the Ferris wheel. The rider is heading towards the top of the Ferris wheel. Determine an equation that models the situation.
d) Draw the graph of the height of a rider vs. time. The graph should have 2 cycles and the graph should start when the rider is halfway between the highest and lowest point in the Ferris wheel. The rider is heading towards the bottom of the Ferris wheel. Determine an equation that models the situation.
To the person who is able to help me, thank you so much. I tried my best and I know that the answers the questions goes as: a) y=-10cos12x+11 b) y=10cos12x+11 c) y=10sin12x+11 d) y=-10sin12x+11
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! since the rider is boarding at the middle between the bottom and the top and heading for the top of the ferris wheel, then the sine function is indicated.
general form of the sine function is y = a * (b * (x - c)) + d
a is the amplitude
b is the frequency
c is the horizontal shift
d is the vertical shift
the period of the cycle needs to be 30 seconds.
that's the time required to make one complete revolution.
frequency = 360 / period = 360 / 30 = = 12
the ferris wheel has a diameter of 20 meters.
that means a radius of 10 meters.
the amplitude of the sine wave is therefore 10 meters.
the center of the circle is 11 meters off the ground.
that means the vertical shift is 11 meters.
there is no horizontal shift.
the sine wave formula becomes y = 10 * sin(12 * x) + 11
that would be selection c.
here's the graph showing 2 cycles of the ferris wheel.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
It seems obvious that the purpose of this exercise is to distinguish among different basic sinusoidal functions. The Ferris wheel is the same in every case; the only difference is where the rider starts -- i.e. where the graph is at the start (at time 0).
The diameter of the Ferris wheel is 20m, so the radius is 10m; and its center is 11m above the ground. That is why all the correct answers show an amplitude of 10 and a vertical shift of 11.
The "12" in all the correct answers is apparently related to the period of 30 seconds for the Ferris wheel, because 12 times 30 is 360, which is the number of degrees in a full revolution. But using degree measure in a sinusoidal function is unusual....
But I don't think we are really concerned with those parameters 10, 11, and 12. What we seem to be concerned with is the difference between the four cases.
The four cases are examples of four basic sinusoidal functions with no horizontal shift. Here are simple graphs of 2 cycles each of the four basic cases:
(1) 
At time 0, at the median value and increasing. This is your case c -- graph starts when rider is at middle height and going up, so case c) is a positive sine function.
(2) 
At time 0, at the median value and decreasing. This is your case d -- graph starts when rider is at middle height and going down, so case d) is a negative sine function.
(3) 
At time 0, at the maximum value. This is your case b -- graph starting when rider is at highest point, so case b) is a positive cosine function.
(4) 
At time 0, at the minimum value. This is your case a -- graph starting when rider is at lowest point, so case a) is a negative cosine function.
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