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1 answer:
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1. See attached picture:
2. Radius of the Ferris wheel is 60/2 = 30 feet.
The center of the Ferris wheel is 30 +2 = 32 feet.
At the bottom you are 2 feet off the ground at 0 seconds.
At 30 seconds you are in line with the center of the Ferris wheel (32 feet).
At 60 seconds (1 minute) you are at the top ( 62 feet ).
At 90 seconds you are in line with the center of the Ferris wheel (32 feet).
At 120 seconds ( 2 minutes) you are back at the bottom (2 feet).
This is a cosine function written as y = Acos(Bx) +C
where A is the amplitude ( the difference between the center and the top written as a negative, which in this case is the radius of the Ferris wheel as a negative.
A = -30
B is found using the period formula 2PI/B , period is the time so you have:
120 = 2PI/B
Multiply both sides by B:
120B = 2PI
Divide both sides by 120:
B = 2PI/120
Simplify:
B = PI/60
C is the center point of the Ferris wheel, which is 32.
The function becomes: Y= -30cos(PIx/60)+32
Now to write as a function of time, replace y with H9t) and x with t:
h(t) = -30cosPIt/60)+32
