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13 August, 21:53

A Ferris wheel is 45 meters in diameter and boarded from a platform that is 2 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).

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  1. 13 August, 23:46
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    - If the wheel rotates clockwise, the height function is

    h (t) = 28.5 + 22.5sin (270 - 36t)

    - If the wheel rotates anticlockwisely, the high function is

    r (t) = 28.5 + 22.5sin (270 + 36t)

    Step-by-step explanation:

    - Centre line of the function

    h = f (t)

    = the height of the center of the ferris wheel

    = 6 + 45/2 = 6 + 22.5 = 28.5 meters.

    - The period of rotation is 10 minutes; so the wheel turns 360/10 = 36 degrees per minute.

    It is not clearly stated if the wheel rotates clockwise or anti-clockwise.

    Let us consider both cases:

    - If it rotates clockwise, the current angle is a = 270 - 36t degrees, where t is the time in minutes.

    Then the height function h = f (t)

    = 28.5 + 22.5sin (a)

    = 28.5 + 22.5sin (270 - 36t)

    - If the wheel rotates anti-clockwise, the current angle is

    b = 270 + 36t degrees.

    Then the height function

    h = r (t)

    = 28.5 + 22.5sin (b)

    = 28.5 + 22.5sin (270 + 36t)
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