Question

A Ferris wheel has a diameter of 60 feet. When you start at the bottom of the Ferris wheel, you
are 2 feet from the ground. The Ferris wheel completes one rotation in 2 minutes.

Create a function that represents your height relative to the center of the Ferris wheel as a
function of time.

*in this question i understand that the diameter is 60 so the center as radius is 30 , but i don't understand how to make it as a function time

Now create a function that represents your height from the ground as a function of time.

* i don't understand this one neither PLEEAASE HEEELP

Answer 1

you have to be familiar with the meaning of the constants in an equation such as
y = a sin k(Ø+d) + c

a is the amplitude, our range of heights is 60 ft
so a = 30
y = 30sin kt + c , where t is in minutes
the lowest value so far would be -30, but we need our lowest to be +2
so c = 32

y = 30 sin k(t+d) + 32

the period of our wheel is 2 minutes, so
2π/k = 2
2k = 2π
k = π

so we have y = 30 sin π(t+d) + 32
we now have to "move" our basic curve d units so that
when t = 0 , we have y = 2
when t = 1/2, we have y = 32
when t = 1 , we have y = 62 ***
when t = 3/2, we have y = 32
when t = 2, we have y = 2
using ***
62 = 30sin π(1+d) + 32
sin π(1+d) = 1
I know sin π/2 = 1
so π(1+d) = π/2
1+d = 1/2 --------> d = -1/2

looks like we have:
<b>y = 30 sin π(t - 1/2) + 32</b>


testing:
when t = 0, y = 30sin -π/2 + 32 = 2 , that's good
when t = 1/2, y = 30sin π(1/2-1/2) + 32 = 32, ok
when t = 1 , y = 30 sin π(1/2) + 32 = 62
looks like we got it!!!