Answer:
y = -10·sin(πt/5) +12
Explanation:
You want the equation of the height of a rider of a Ferris wheel that has a radius of 10 and is 2 off the ground, with a period of 10 seconds, moving downward, starting from even with the center.
Equation
The general form of the equation will be ...
y = A·sin(2πt/T) + B
where A is a scale factor that is based on the radius and initial direction, and B is the height of the center of the wheel above the ground.
Height
We assume that 2 [units] off the ground means the low point of the travel is at that height. Then the middle of the wheel is those 2 [units] plus the radius of the wheel:
B = 2 + 10 = 12
Scale factor
The scale factor A will be the radius of the wheel, made negative because the initial direction is downward from the initial height. That is, ...
A = 10
Period
The period (T) is given as 10 seconds.
Height function
Putting these parameters together gives ...
y = -10·sin(2πt/10) +12
y = -10·sin(πt/5) +12
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Additional comment
We wonder if this wheel is really only 20 inches (20 in) in diameter, as that dimension seems suitable only for a model. We suspect it is probably 20 meters (20 m) in diameter.
Sometimes "m" is confused with "in" when it is written in Roman font and reproduced with poor resolution.
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