A ferris wheel is 40 meters in diameter and boarded from a platform that is 1 meters above the ground.The six o’clock position on the

A ferris wheel is 40 meters in diameter and boarded from a platform that is 1 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 4 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).

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  1. t = 2.9517 min

    Step-by-step explanation:

    Given

    D = 40 m ⇒ R = D/2 = 40 m/2 = 20 m

    ybottom = 2 m

    ytop =  ybottom + D = 40 m + 2 m = 42 m

    yref = 34 m

    t = 10 min

    The height above the ground (y) is a sinusoidal function.

    The minimum height is ybottom = 2 m

    The maximum height is ytop = 42 m;

    The midline is (ybottom + ytop)/2 = (2 m + 42 m)/2 = 22 m

    If we model the wheel as follows

    x² + y² = R²

    where

    y = yref - (R + ybottom) = 34 m - (20 m + 2 m) = 12 m

    R = 20 m

    we have

    x² + (12 m)² = (20)²

    ⇒ x = 16 m

    then

    tan (θ/2) = x/y

    ⇒ tan (θ/2) = 16 m/12 m

    ⇒ θ = 106.26°

    Knowing the angle of the circular sector, we apply the relation

    t = (106.26°)*(10 min/360°)

    ⇒ t = 2.9517 min

    Since the period of revolution is 10 minutes, the ride is above 34 meters for 2.9517 minutes each revolution.

  2. t >.696 minute

    Step-by-step explanation:

    Given,   r = 40 m

    [tex]p=2\pi r[/tex]

    [tex]p=80\pi[/tex]

    Given,     t = 5 min for one revolution

    [tex]v=p/t[/tex]

    [tex]80\pi /5= 16\pi[/tex]

    time to reach to more than 35 m

    [tex]35< 16\pi t[/tex]

    [tex]t 35/16\pi[/tex]

    [tex]t .696 min[/tex]

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