A sinusoidal equation can be used to describe the height because the height depends on a periodic motion, and the equation can be written as:
h(t) = 13ft*sin(pi*t) + 24ft
Why a sinusoidal equation can be used?
Remember that the sine function has a periodicity, such that:
sin(x + 2pi) = sin(x).
So, for a circle where if you do a complete rotation you end in the initial place, so there can be a relation between the height and a sinusoidal equation.
Notice that the initial position is 24ft above the ground, so we can write this, at the moment, as:
h(x) = Asin(n*t) + 24ft
A is the amplitude, it defines the maximum height and minimum height, both depend on the radius (the maximum height is 24ft plus the radius, the minimum height is 24ft minus the radius) then we write:
h(t) = 13ft*sin(kt) + 24ft
k depends on how much time takes to do a full rotation. We know that the sine function does a "complete cycle" in 2pi, while the wheel does a full rotation in 2 seconds, then we have that:
k*2 = 2pi
k = (2pi)/2s = pi
Then the sinusoidal equation that represents the height is:
h(t) = 13ft*sin(pi*t) + 24ft
If you want to learn more about sinusoidal equations, you can read:
https://brainly.com/question/9478364
