A Ferris wheel has a diameter of 40 meters and rotates at a constant speed completing one full revolution every 2 minutes. If a person gets on the Ferris wheel at the bottommost point, express the person's height above the ground as a function of time, assuming the center of the Ferris wheel is at ground level.
A Ferris wheel has a diameter of 40 meters and rotates at a constant speed completing one full revolution every 2 minutes. If a person gets on the Ferris wheel at the bottommost point, express the person's height above the ground as a function of time, assuming the center of the Ferris wheel is at ground level.
Answer: The Ferris wheel has a diameter of 40 meters, which means the radius (r) is half of the diameter, i.e., (r = 20) meters. The Ferris wheel completes one full revolution every 2 minutes. The period (T) of the Ferris wheel is the time it takes to complete one full revolution. In this case, T = 2 minutes. The angular frequency (w) can be calculated using the formula (w = 2/?). Substituting the given value for (T): w = 2/? = ? radians per minute. Now, the height (h) of the person above the ground as a function of time (t) can be expressed using a sine function. The general form of a sine function is h(t) = A sin(wt+ϕ)+C where: - A is the amplitude (half the range of the function), - w is the angular frequency, - ϕ is the phase shift, - C is the vertical shift. In this case, since the person starts at the bottommost point, there is no phase shift (ϕ = 0), and the vertical shift (C) is equal to the radius of the Ferris wheel (20) meters). So, the height function is h(t) = 20 sin (?t) +20
- using this question and answer make a labeled diagram of the ferris wheel and make a visual answer ( explain with hand drawn images on whats going on )
![A Ferris wheel has a diameter of 40 meters and rotates at a constant speed completing one full
revolution every 2 minutes. If a person gets on the Ferris wheel at the bottommost point,
express the person's height above the ground as a function of time, assuming the center of the
Ferris wheel is at ground level.
Answer:
The Ferris wheel has a diameter of 40 meters, which means the radius (r) is half of the diameter,
i.e., (r = 20) meters.
The Ferris wheel completes one full revolution every 2 minutes. The period (T) of the Ferris
wheel is the time it takes to complete one full revolution. In this case, T = 2 minutes.
The angular frequency (w) can be calculated using the formula (w = 2/7). Substituting the given
value for (T):
w = 2/π = π radians per minute.
Now, the height (h) of the person above the ground as a function of time (t) can be expressed
using a sine function. The general form of a sine function is h(t) = A sin(wt+)+C
where:
A is the amplitude (half the range of the function),
w is the angular frequency,
- is the phase shift,
- C is the vertical shift.
In this case, since the person starts at the bottommost point, there is no phase shift (p = 0), and
the vertical shift (C) is equal to the radius of the Ferris wheel (20) meters).
So, the height function is h(t) = 20 sin (nt) +20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f8bc090-31c3-43b5-8eff-fe1e3cfd2087%2Fbfccb412-e0e0-4aab-a862-5558ff0eb013%2Fo7wg4_processed.png&w=3840&q=75)
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