A ferris wheel is 20 meters in diameter and boarded at its lowest point (6 O\'Cl

Question

A ferris wheel is 20 meters in diameter and boarded at its lowest point (6 O'Clock) from a platform which is 6 meters above ground. The wheel makes one full rotation every 18 minutes, and at time t=0t=0 you are at the loading platform (6 O'Clock). Let h=f(t)h=f(t) denote your height above ground in meters after tt minutes.

(a) What is the period of the function h=f(t)h=f(t)?
period =

(b) What is the midline of the function h=f(t)h=f(t)?
y=

(c) What is the amplitude of the function h=f(t)h=f(t)?
amplitude =

Explanation / Answer

20 m in diameter
lowest pt at 6 o clock
Lowest pt is 6 m above grnd

Total ht to the top is 6 + 20 = 26

Min = 6
Max = 26

So, amplitude, A = (max - min)/2
= (26 - 6)/2
= 10

D = midline = (max+ min)/2
D = (6 + 26)/2
D = 16

Period = 18 min
So, B = 2pi/18
B = pi/9

And now, lowest at the start
So, this is negative cos
and we have C = 0

So using
y = -Acos[B(x - C)] + D

y = -10cos[pi/9(x - 0)] + 16

y = -10cos(pi*x/9) + 16 ----> ANS

a) period = 18 min
b) midline = 16
c) amplitude = 10

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