PLEASE READ THE BOTTOM I ADDED ON!! :) the ferris wheel at an amusement park measures 16m in diameter. the wheel does 3 rotations every minute. the bottom of the wheel is 1m above the ground...
a) determine the simplest equation that models Megan's height above that ground(h) over time (t). give 2 more equations that model the situation. please explain! :)
I need a cosine equation and why is the period 20 mins shouldn't it be 0.33, aren't u you suppose to divided 1 by 3 to get 0.33 as ur period (1 rotation per a min)
see related questions below. If you're still stuck, show us your work and your sticking point.
period 1/3 = 0.333 (1 revolution per a min)
k=2pi/1/3
= 6 pi
isnt that the k value why would it be 1/10 pi
You have figured the period in hours. Reiny did it in minutes, so his period is 6pi/60 = pi/10
sorry. You did yours in minutes. He did his in seconds, but the ratio is the same.
oh okay thank you makes sense now! would it just be 8 cos (pi/10) +9 for the cosine equation? and what would the period be in seconds? and would that effect the question? cause the next question what is her height after 25 secs
Opss i didnt read that, i just refreshed the page! okok, so reiny did it in secs. but for cosine equation would it be 8 cos (pi/10) +9 or different
wait but why did reiny write 20 mins for the period?
sorry about the confusion , I just look back at my solution, that should have been 20 seconds
(at 3 rotations per minute --> 1 rotation in 20 seconds)
the math stays the same, t is in seconds
To determine the simplest equation that models Megan's height above the ground (h) over time (t), we can consider the height of the Ferris wheel as it rotates.
Let's break down the problem step by step:
1. The diameter of the Ferris wheel is given as 16 meters. The radius of the wheel is half of the diameter, so the radius would be 8 meters.
2. The bottom of the wheel is 1 meter above the ground. This means when Megan is at the bottom, her height above the ground would be 1 meter.
3. The Ferris wheel completes 3 rotations every minute. This means that in 1 minute, Megan will be at the bottom of the wheel three times.
Now, let's derive the equation:
A sine or cosine function will be appropriate to model the periodic nature of Megan's height as the Ferris wheel rotates.
If we choose a cosine function, it would be of the form:
h = A * cos(B * t - C) + D
Where:
- A represents the amplitude, which indicates the maximum vertical distance from the average height.
- B determines the frequency of oscillation. The period of the function can be calculated as T = 2π / B.
- C is the phase shift, which determines the horizontal displacement of the function.
- D represents the vertical shift, which indicates the average height of the function.
Since Megan starts at the bottom of the wheel (1 meter above the ground), the vertical shift (D) would be 1.
To calculate the period, T, we can use the fact that the wheel completes 3 rotations in 1 minute:
T = 1 minute / 3 rotations = 1/3 minutes = 20 seconds
Therefore, B = 2π / T = 2π / 20 = π / 10.
Plugging in the values, our equation becomes:
h = A * cos((π / 10) * t - C) + 1
There can be additional equations depending on the specific information given or what you want to model. For example:
1. Equation relating the height of the wheel to the angle of rotation:
h = r * cos(θ) + 1
This equation uses the angle of rotation (θ) instead of time (t) to represent Megan's height.
2. Equation relating the height of the wheel to the number of rotations:
h = r * cos(2πn) + 1
This equation uses the number of rotations (n) instead of time (t) to represent Megan's height.
Please note that while the period of one rotation is indeed 0.33 minutes (1/3), we need to consider the period for one full ride, which consists of three rotations, hence 20 seconds or 1/3 minutes.
I hope this explanation helps! Let me know if you have any further questions.