Mathematics, 20.07.2019 16:30 zaniyastubbs9

Will make ! a ferris wheel has a diameter of 220 feet and the center of the wheel is 125 feet above the ground. the wheel makes a complete turn every 2 minutes. write a cosine function to express the height h (in feet) of a passenger on the wheel as a function of time t (in minutes) ), given that the passenger is at the lowest point on the wheel when t=0

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Since the radius of a circle is half its diameter, the radius of our Ferris wheel is $r= \frac{220}{2} =110$ ft

Next, we are going to convert from revolutions per minute to degrees per second.
We know that the wheel makes a complete turn every 2 minutes, so it makes a complete turn in 120 seconds. Since there are 360° in a complete turn, we can set up our conversion factor:
$\frac{1*360}{120}=3$ degrees per second

Now, lets find the height:
We know that the passenger is at the lowest point on the wheel when t=0; since the wheel is 125 feet above the ground, at t=0 h=125. To find t at the top, we are going to take advantage of the fact that the wheel will turn 180° from the lowest point to the top and that it turns 3° every second:
$t= \frac{180}{3}$
t=60

Notice that the height at the top is the diameter of the wheel plus the height above the ground, so h=220+125=345

.

To model the situation we are going to use the cosine function, but notice that $cos (\alpha)$ is 1 when $\alpha =0$ and -1 wen $\alpha =180$ . Since we want the opposite, we are going to use negative cosine.
Notice that we want $\alpha =180$ when t=60

, so we are going to use -cos(3t)

. Next, we are going to multiply our cosine by the radius of our wheel: -110cos(3t)

, and last but not least we are going to add the sum of the radius of the wheel plus the height above the ground:
h=110+125-110cos(3t)

Now that we have our height function lets check if everything is working:
the passenger is at the lowest point at t=0; we also know that the lowest point is 125 feet above the ground, so lets evaluate our function at t=0:
h=225-110cos(3t)

feet
So far so good.
We also know that at t=60, our passenger is 345 feet above the ground, so lets evaluate our function at t=60 and check if coincides:
h=225-110cos(3t)

feet

We can conclude that cosine function that express the height h (in feet) of a passenger on the wheel as a function of time t (in minutes) ) is: h=225-110cos(3t)

Answer from: Quest

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Answer from: Quest

you estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82 .the total height of the building is another 123 meters above the 86th floor.

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Will make ! a ferris wheel has a diameter of 220 feet and the center of the wheel is 125 feet above...