Ferris wheel position

Asked by maham237 @ in Mathematics viewed by 260 People

HELPHELP
A ferris wheel is 30 meters in diameter and boarded from a platform that is 5 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 10 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).

Answered by maham237 @


Answer:

h = f(t) = -15cos((π/5)t) +20

Step-by-step explanation:

If you like, you can make a little table of positions:

(t, h) = (0, 5), (5, 35)

Since the wheel is at an extreme position at t=0, a cosine function is an appropriate model:

h = Acos(kt) +C

The amplitude A of the function is half the difference between the t=0 value and the t=5 value:

A = (1/2)(5 -35) = -15

The midline value C is the average of the maximum and minimum:

C = (1/2)(5 + 35) = 20

The factor k satisfies the relation ...

k = 2π/period = 2π/10 = π/5

So, the function can be written as ...

h = f(t) = -15cos((π/5)t) +20


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