Let's assume that the Ferris wheel is a perfect circle and that your starting position is at the bottom.
The height of the Ferris wheel can be modeled by a sinusoidal function of time t.
At t=0 seconds, your initial height is 1 foot above the ground, which corresponds to the amplitude of the function.
The period of the function is the time it takes for the Ferris wheel to complete one revolution, which is 30 seconds. Therefore, the period is T=30.
The midpoint of the function is the average of the highest and lowest points, which is (99+1)/2=50 feet. Thus, the vertical shift of the function is 50.
Since you start at the bottom of the Ferris wheel, the function should start at its minimum point.
Putting all of this together, we get:
h(t) = -49cos((2π/30)t) + 50
where h(t) is your height above the ground in feet at time t in seconds.
Note that the negative sign in front of the cosine function is necessary to ensure that the function starts at its minimum point.