We have two responses for you, Anthony:
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Hi Anthony,
I would set up a coordinate system with the origin at the centre of
the ferris wheel. Suppose you are at the point P(x,y) on the wheel in
the diagram.
![.](anthony1.1.gif)
Since the diameter of the wheel is 250 feet its radius is 125 feet
and the height you are above the ground is h = y + 125 + "the
distance the base of the wheel is above the ground". From the diagram
y = 125 sin(theta) and hence all that remains in finding the height
at time t is to find theta at time t. You know that the wheel rotates
360 degrees every 40 seconds so in t seconds the wheel rotates 360/40
= 9 t degrees.
I hope this helps,
Penny
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If you need more help, Sue gives a bit more detail:
Hi Anthony.
The path of the seat on the ferris wheel is circular. That means that
if you were to graph the position of the seat, you could create a
circle centered at the origin. The radius would be the radius that
the seat moves, which is 2 feet less than the radius of the ferris
wheel itself.
Now, the height is the y axis. You probably already know that the
equation for the y coordinate of a R-radius circle at the origin is
(RcosA, RsinA) where A is the angle from the horizontal. But let's
say you want to measure the angle from the bottom instead, going
clockwise. What would be the coordinates then? When A is 0, we want
(0, -R) and when A is 90 degrees, we want (-R, 0). If we said
(-RsinA, -RcosA), we would have the right co-ordinates. At 180
degrees, this is (0, R) and at 270 degrees it is (R, 0) as we hoped.
![.](anthony1.2.gif) ![.](anthony1.3.gif)
So we know the co-ordinates. The height is the y co-ordinate: -RcosA.
Now if we draw the ground, it should be a horizontal line 4 feet below
the bottom of the seat (because the bottom of the ferris wheel is 2
ft above the ground and the seat is 2 ft above that).
![.](anthony1.4.gif)
But since we want the ground to be at zero height, let's shift the
whole graph up until that horizontal ground line is on top of the x
axis. How far did we shift it? R + 4 units up. So really we added R
+ 4 units to the y co-ordinate which we said earlier was -RcosA.
![.](anthony1.5.gif)
This means that the height is R + 4 - RcosA. where A is the angle from
the bottom.
Hope this helps.
Stephen La Rocque.
![.](anthony1.6.gif)
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