A vacationer sits all day on the corner of a pier in New Yor

A vacationer sits all day on the corner of a pier in New York Harbor and notices that at 9 am, when the water level is at its lowest, the water\'s depth is 4 feet. At 3 pm, the water has risen to its maximum depth of 16 feet. If the depth of the water level varies periodically, let f(t) be the formula the depth of the water, in feet, as a function of time t, in hours past 9 am. Create a formula for f(t) using cosine. (Caution: how is a full period?) A Ferris wheel is 45 meters in diameter, and must be boarded from a platform that is 2.5 meters above the ground. The wheel makes complete revolution every 20 minutes. At the initial time t = 0, you are the 12:00 position. If h(t) gives your height above ground level t minutes after the initial time, the midline of h(t)is y = _____. The graph below shows your height h = f(t) in meters t minutes after a Ferris wheel ride begins. How many meters high is the center of the Ferris wheel?

Solution

1)comparing with f(t)=Acos(Bt) +k

time between maximum and minimum depths=6 hours

period =2*6

2_/B=2*6

B=_/6

k=(16+4)_/2=10

f(t)=Acos((_/6)t) +10

at t=0, f(0)=4

Acos((_/6)*0) +10=4

A+10=4

A=-6

f(t)=-6cos((_/6)t) +10

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2)minimum of h(t)=2.5 m

maximum of h(t)=2.5+45=47.5 m

midline of h(t):

y=(47.5+2.5)_/2

y=25

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