A double Ferris wheel has a 40 meter rotating arm attached at its center to a 50 meter main support.
At each end of the rotation arm, there's another Ferris wheel measuring 24 meters in diameter. These wheels, in addition to the main wheel, all rotate counterclockwise.
The rotating arm takes 9 minutes to complete one full revolution, and each wheel takes 6 minutes to complete a revolution about that wheel's hub.
At time t=0, the rotating arm is parallel to the ground, and our seat is at the 3 o'clock position of the rightmost wheel
What is the formula for h=f(t) as function of time in minutes?
At each end of the rotation arm, there's another Ferris wheel measuring 24 meters in diameter. These wheels, in addition to the main wheel, all rotate counterclockwise.
The rotating arm takes 9 minutes to complete one full revolution, and each wheel takes 6 minutes to complete a revolution about that wheel's hub.
At time t=0, the rotating arm is parallel to the ground, and our seat is at the 3 o'clock position of the rightmost wheel
What is the formula for h=f(t) as function of time in minutes?
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The Ferris wheel is an example of uniform circular motion. The height as a function of time is described by a sine function. (For example see http://mathworld.wolfram.com/UniformCirc...
The rotating arm takes 9 minutes to complete a revolution so its angular velocity is 2π/9. Since the arm has a radius of 20, starts outs horizontal with us on the right, and is rotating counterclockwise, its height relative to the top of the main support is given by 20sin(2πt/9). Similarly the height of our seat relative to the center of the wheel we are on is given by 12sin(2πt/6). The height of the main post is 50. Putting all these together and simplifying:
h(t) = 50+20sin(2πt/9)+12sin(πt/3)
where h is in meters and t is in minutes.
The rotating arm takes 9 minutes to complete a revolution so its angular velocity is 2π/9. Since the arm has a radius of 20, starts outs horizontal with us on the right, and is rotating counterclockwise, its height relative to the top of the main support is given by 20sin(2πt/9). Similarly the height of our seat relative to the center of the wheel we are on is given by 12sin(2πt/6). The height of the main post is 50. Putting all these together and simplifying:
h(t) = 50+20sin(2πt/9)+12sin(πt/3)
where h is in meters and t is in minutes.