Ferris Wheel Function

Hey its Anthony. I'm representing group 1.

Diameter of wheel: 100ft.
Seat is 3ft. off ground
Technically max height is actually 100ft. + 3ft. 103ft.
Period: 4/60 ---> 1/15 (1cycle per 15 sec)

a) Write two equations, one sine and one cosine, that would represent the distance above the ground as a function of time. Let t = 0 when the seat is at the lowest point on the wheel.

b) How high will a person be 10 seconds after they begin riding the ferris wheel?

c) How long after a person gets on the ride will they actually be 100 feet in the air?

d) How long, during each revolution, is a person more than 60 feet in the air?thanks group 6, i borrowed your image and i am acknowledging you guys now.


a) sine
a: 50
b: 2π/15
c: 15/4
d: 53

cosine
-50
2π/15
zero
53

50sin[2π/15(x-15/4)] +53
-50cos 2π/15x+53


b) h(x) = 50sin[2π/15(x-15/4)] +53
H(10) = 50sin[2π/15(10-15/40]+53

h = 78 ft.

c) the wheel completes 1 revolution every 15 seconds. The height of the seat on the wheel climbs and reaches its maximum at half the period which is 15s/2. After reaching its max. of 103ft. it starts to decline back down to its min. which is 3. from min to min (trough to trough) is one cycle. therefore it reaches its max at 7.5 seconds.

d) T(x) = 50sin[2π/15(x-15/4)] +53
let θ = [2π/15(x-15/4)]
60 = 50sinθ +53
7 = 50sin θ
7/50 = sin θ

3.0011, 0.1405 = θ

2π/15(x-15/4) = θ
x - 15/4 = 0.1405(15/2π) x = 0.3353 + 15/4 x = 4.0853


2π/15(x-15/4) = = 3.0011
x - 15/4 = 3.0011(15/2π)
x = 7.1646 +15/4
x = 10.9147

10.9147 - 4.0853 = 6.8293s

a person is more than 60 feet in the air for roughly 7 seconds during each revolution.