Diameter is 135 meters and makes one revolution every 30 minutes. Find a sinsuoid which models the height h of the passenger above the ground in meters t minutes after they board.

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hesgidiauE · Accepted Answer

A sinusoidal function is of the form h=asin⁡bt+d or h=acos⁡bt+d where ∣a∣ is the amplitude, 2πb is the period, and dd is the vertical shift (its midline). The diameter of the wheel is twice the amplitude. Since the diameter of the wheel is 135 meters, then the amplitude is ∣a∣=135.2=67.5. Since the wheel starts at the ground, then the center point of the wheel is the vertical shift of the sinusoid. Since the radius of the wheel is 67.5 m, then the vertical shift is d=67.5. The wheel makes one revolution every 30 minutes so the period is 30. Therefore 2π/b=30. Solving this for bb gives b=2π/30=π/15b.  A since curve starts at its midline and a cosine curve starts at its maximum. Since we need the function to start at the ground, which is the minimum of the function, we need to use the cosine form and we need a&amp;lt;0 so the function will start at the minimum instead of the maximum. Therefore a=−67.5   We now have everything we need to write the function. Substituting a=−67.5,b=π15  and d=67.5 intoh=acos⁡bt+d then gives h=−67.5cos⁡(π/15)t+67.5.

Diameter is 135 meters and makes one revolution every 30 minutes. Find a sinsuoid which models the height h of the passenger above the ground in meters t minutes after they board.

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