A ferris wheel has a radius of 25 feet. A person takes a seat, and the wheel turns 5pie/6 radians. How far is the person above the ground? please explain to me how to solve this
We are to suppose the person got on the wheel at the very bottom.
You might want to convert this to degrees if you wish, unless the exercies must be done in radians. We'll also suppose the wheel is going conterclockwise, but the answer doesn' matter -it should be the same regardless of which side of the wheel we're observing.
You should be able to see that the wheel has rotated pi/4 + pi*7/12 = pi*5/6 radians, thus it has rotated at least 25 feet up. Now add 25*sin(pi*7/12) to 25. Be sure to draw a diagram to see what is happening here. I left it in radians, but you could convert and solve in degrees too.
I think I did the wrong calculations here. When it rotates pi/2 then it's 25ft off the ground
We also have pi*5/6 - pi/2 = pi/3. So pi/3 of 60deg is the angle the seat now make with the horizontal. The height is then
25*sin(60)ft + 25ft = 25(1+sqrt(3)/2)ft
It looks to be approximately 46.7ft
I mistook pi/4 for 1/4 of a turn, oops!
why is latin a big part of english?
A Ferris wheel has a deameter of 50m. The platform at the bottom, where you load the ferris wheel, is 3 m above the ground. The Ferris wheel rotates three times every two minutes. A stopwatch is started and you notice you are even with the center of the ferris wheel, going down when the watch is at 4 seconds. write an equation that expreses your height as a function of elapsed time.
wtf
To write an equation that expresses your height as a function of elapsed time, we can start by determining the period of rotation for the Ferris wheel.
Given that the Ferris wheel rotates three times every two minutes, we can calculate the period (T) of rotation as follows:
T = (2 minutes) / (3 rotations)
T = 2/3 minutes
Now, let's define the height function as h(t), where t is the elapsed time in seconds.
Since the platform at the bottom of the Ferris wheel is 3 meters above the ground, we need to subtract this constant height from the total height to get the variable part that changes with the rotation.
Considering that the Ferris wheel takes 2/3 minutes (or 40 seconds) for one complete rotation, the height of the person at the center (even with the center of the Ferris wheel) occurs halfway through this period, which is at 20 seconds.
We can then write the equation as follows:
h(t) = 0 if t < 4
h(t) = -3 meters if 4 <= t < 20
h(t) = -3 meters + (50/2) meters * cos((2π/40)(t-20)) if t >= 20
In this equation, the cosine function represents the up and down motion of the person as the Ferris wheel rotates. The amplitude of the cosine function is (50/2) meters since the radius of the Ferris wheel is 25 meters.
Please note that this equation assumes the person starts at the bottom of the Ferris wheel and that the Ferris wheel rotates counterclockwise.
To write an equation that expresses your height as a function of elapsed time, we need to consider the distance traveled by the Ferris wheel in relation to the time elapsed.
First, let's determine the period of the Ferris wheel, which is the time it takes for the wheel to complete one full revolution. We are given that the Ferris wheel rotates three times every two minutes. Since there are 60 seconds in a minute, this means the wheel takes (2 minutes) x (60 seconds/minute) = 120 seconds to complete three rotations. Therefore, the period of the Ferris wheel is 120 seconds.
Next, let's determine the height of the platform. We know that the platform is 3 meters above the ground.
Now, let's define our variables. Let h(t) represent your height above the ground at time t, and let t be the elapsed time in seconds.
To find the equation, we need to determine the relationship between the angle of rotation and the corresponding height. Since the Ferris wheel has a diameter of 50 meters, the radius will be half of that, which is 25 meters.
As the Ferris wheel rotates, your height will vary sinusoidally based on the angle of rotation. The equation for the height can be written as:
h(t) = A * sin(B * t + C) + D
Where:
- h(t) is the height above the ground at time t
- A is the amplitude of the sinusoidal function, which is the maximum height variation
- B is the frequency of the function, which determines how quickly the height oscillates
- C is the phase shift of the function, which determines the starting point of the height variation
- D is the vertical shift of the function, which represents the base height (in this case, the platform height)
To find the values of A, B, C, and D, we can relate them to the characteristics of the Ferris wheel.
The amplitude, A, is half of the diameter of the Ferris wheel, which is 25 meters.
The frequency, B, is determined by the period of the Ferris wheel. Since the period is 120 seconds, we can use the formula B = 2π / T, where T is the period. Plugging in the values, we have B = 2π / 120 = π / 60.
The phase shift, C, is determined by the starting angle of the wheel when the stopwatch is at 4 seconds. Since we start at the bottom of the wheel and go down, the phase shift will be at the maximum height, which is π/2 radians.
The vertical shift, D, is the height of the platform, which is 3 meters.
Putting it all together, the equation that expresses your height as a function of elapsed time is:
h(t) = 25 * sin((π / 60) * t + π/2) + 3
This equation will give you the height above the ground at any given time t, measured in seconds.