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).

  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

The equation of the function of the height in meters above the ground t minutes after the wheel begins to turn, is presented as follows;

The process for finding the above function is as follows;

The given parameters of the Ferris wheel are;

The diameter of the Ferris wheel, D = 30 meters

The height of the Ferris wheel above the ground, d = 5 meters

The level of loading the platform = The six o'clock position

The time it takes the wheel to make one full revolution, T = 10 minutes

The required parameter;

The function which gives the height, h, of the Ferris wheel = f(t)

Method;

The equation that can be used to model the height of the Ferris wheel is the sine function which is presented as follows;

y = A·sin[k·(t - b)] + c

Where;

A = The amplitude = (highest point - Lowest point)/2

∴ A = (35 - 5)/2 = 15

The period, T = 2·π/k

∴ 10 minutes = 2·π/k

k = 2·π/10 = π/5

k = π/5

At the starting point, the Ferris wheel is at the lowest point, and t = 0, we have;

The sine function is at the lowest point when k·(t - b) = -π/2

Therefore, we get;

π/5·(0 - b) = -π/2

-b = -π/2 × (5/π) = -5/2 = -2.5

b = 2.5

The vertical shift, c = (Max - Min)/2 + Min = (Max + Min)/2

∴ c = (35 + 5)/2 = 20

c = 20

The equation of the Ferris wheel of the form, y = A·sin[k·(t - b)] + c, is therefore;

Learn more about the Ferris wheel equation here;

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step-by-step explanation:

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