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A ferris wheel is 50 meters in diameter and boarded from a platform that is 4 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 6 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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lublana

Answer:

[tex]h(t)=-25cos(\frac{\pi}{3}t)+29[/tex]

Step-by-step explanation:

We are given that

Diameter,d=50 m

Distance of platform from the ground=4 m

Amplitude,A =[tex]\frac{diameter}{2}=\frac{50}{2}=25 m[/tex]

Midline,C=Amplitude+Distance from the ground=25+4=29 m

Period,T=6 minutes

We know that period of cosine

[tex]\frac{2\pi}{b}=T=6[/tex]

[tex]b=\frac{2\pi}{6}=\frac{\pi}{3}[/tex]

[tex]h(t)=-Acos(bt)+C[/tex]

Substitute the values

[tex]h(t)=-25cos(\frac{\pi}{3}t)+29[/tex]