In a short bond paper, formulate a real-life problem that can be modeled by circular function. The following information must be present:

Real-life problem that can be modeled by circular function:

Suppose a Ferris wheel has a diameter of 50 meters and rotates once every 2 minutes. When the ride starts, the bottom of one of the cars is at a height of 5 meters above the ground.

1. Equation of the problem being modeled:
Let h(t) be the height of the bottom of the car above the ground at time t in seconds. Since the Ferris wheel rotates in a circular motion, the height can be modeled by a sinusoidal function.

Thus, the equation of the problem being modeled is:
$h\left(t\right)=A\sin (\omega t)+c$

Where A is the amplitude, ω is the angular frequency, c is the vertical shift (constant) and t is the time in seconds.

2. Amplitude:
The amplitude represents the maximum displacement from the mean position. In this case, the mean position is the height of the car when it is at its lowest point.

Since the diameter of the Ferris wheel is 50 meters, the radius is 25 meters. Thus, the maximum displacement from the mean position is equal to the radius of the Ferris wheel.

Therefore, the amplitude A is equal to 25 meters.

3. Period:
The period represents the time it takes for one complete cycle of the sinusoidal function. In this case, the period is equal to the time it takes for the Ferris wheel to make one full rotation.

Since the Ferris wheel rotates once every 2 minutes, the period T is equal to 120 seconds.

4. Frequency:
The frequency represents the number of cycles per unit time. In this case, the frequency f is equal to the reciprocal of the period T.

Thus, the frequency f is equal to:

$f=\frac{1}{T}=\frac{1}{120}=0.008333Hz$

5. Constants c/d:
The constant c represents the vertical shift of the sinusoidal function. In this case, the vertical shift is equal to the height of the car when it is at its lowest point, which is 5 meters.

Thus, the constant c is equal to 5 meters.

The constant d represents the phase shift of the sinusoidal function. In this case, there is no phase shift since the ride starts when the bottom of one of the cars is at its lowest point.

Therefore, the constant d is equal to 0.

In conclusion, the height of the bottom of the car above the ground at time t in seconds can be modeled by the circular function:

$h\left(t\right)=25\sin \left(0.05236t\right)+5$

where A = 25 meters is the amplitude, $\omega =0.05236\frac{rad}{s}$ is the angular frequency, c = 5 meters is the vertical shift, and d = 0 is the phase shift.