Question

A ferris wheel is 20 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).

Answer 1

Let's use a sine curve, we could use a cosine as well
amplitude is 10, so h = 10sin kt
the period is 6 minutes, so
2?/k = 6 ----> k = ?/3
sofar: h = 10sin (?/3 t)
this has a min of -10, but our min is to be +1, so we have to raise everything up by 11
so far: h = 10sin(?/3 t) + 11

let's see this through one cycle:
t = 0 , h = 0+11 = 11
t = 1.5 , h = 10 + 11 = 21
t = 3 , h = 0 + 11 = 11
t = 4.5 , h = -10+11 = 1
t = 6, h = 11
sketch this curve.
notice our min is at t = 4.5 or at t = -1.5
But we want our min to be at t = 0, so we could move our curve 1.5 to the right, or 4.5 to the left

y = 10 sin ?/3(t - 1.5) + 11
or
y = 10sin ?/3(t + 4.5) + 11


test both equations for t = 0, 1.5, 3, 4.5, and 6

check:
http://www.wolframalpha.com/input/?i=plot+y+%3D+10+sin+(%CF%80%2F3(t+-+1.5))+%2B+11,+y+%3D+10+sin+(%CF%80%2F3(t+%2B+4.5))+%2B+11

(notice that the two curves coincide and are correct, also notice I had to put in extra brackets)