Question

a ferris wheel with a radius of 14m makes one revolution every 30 seconds. the bottom of the wheel is 2.5m above the ground.
a) find the equation
b) how does the equation change if the graph starts at the centre of rotation

Answer 1

I will assume you want the initial position to be 2.5 m high

Let's start with the basic curve.
amplitude = 7,
period = 2π/k
2π/k = 30
k = π/15

height = 7sin((π/15)t) , where t is in seconds

make a sketch of this to see that at ..
t=0, h = 0
t = 7.5, h = 7sin(π/2) = 7
t = 15, h = 0
t = 22.5 , h = -7

we want our min to happen when t = 0, so move the curve 7.5 to the right
(or 22.5 to the left)
y = 7sin((π/15)(t-7.5) )
but when t = 0, we want that min of -7 to be 2.5

final curve :
h = 7sin((π/15)(t-7.5) ) + 9.5

adjust my equation for b)

Answer 2

or, since the min occurs at t=0,
h = 9.5 - 7cos((π/15)t)