whobatman
Please Help?! It might be a little hard but I will upvote if it's right!!
The Colossus Ferris wheel debuted at the 1984 New Orleans World’s Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride.
Sine function model: h=82.5 sin 3pi (t+0.5)+97.5 where h is the height of the passenger above the ground measured in feet and t is the time of operation of the ride in minutes.
1. What is the period of the sine function model? Interpret the period you found in the context of the operation of the Ferris wheel.
2. The duration of the ride is 15 min.
(a) How many times does the last passenger who boarded the ride make a complete loop on the Ferris wheel?
(b) What is the position of that passenger when the ride ends?
3. A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: h=82.5 sin 3pi (t+0.5)+97.5 where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes.
(a) What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model.
(b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
To answer these questions, we will use the given sine function model:
h = 82.5 sin(3π(t + 0.5)) + 97.5,
where h is the height of the passenger above the ground measured in feet, and t is the time of operation of the ride in minutes.
1. The period of a sine function is the length of one complete cycle. In this case, the coefficient of t in the argument of the sine function is 3π. The period can be found by dividing 2π by the coefficient, so the period is 2π / (3π) = 2/3 minutes.
Interpretation: The period represents the time it takes for the Ferris wheel to complete one full revolution. In this case, the Ferris wheel completes one revolution every 2/3 minutes.
2. (a) The duration of the ride is 15 minutes. To find the number of complete loops made by the last passenger who boarded the ride, we need to divide the duration by the period.
Number of complete loops = 15 / (2/3) = 15 * (3/2) = 22.5.
Since we cannot have half a loop, the last passenger makes 22 complete loops on the Ferris wheel.
(b) When the ride ends after 15 minutes, the position of the last passenger who boarded the ride can be found by evaluating the sine function model at t = 15.
h = 82.5 sin(3π(15 + 0.5)) + 97.5 = 82.5 sin(3π * 15.5) + 97.5.
Calculate this value to find the exact position of the passenger when the ride ends.
3. (a) To find the height of the last passenger at the moment of the power outage, we need to evaluate the sine function model at t = 6.
h = 82.5 sin(3π(6 + 0.5)) + 97.5.
Calculate this value to find the height of the passenger at that moment.
(b) The last passenger to board the ride will not need to wait in order to exit the ride. This is because when the power outage occurs, the last passenger's cage is cranked into the lowest position, which means they will already be at ground level or very close to it. So they can safely exit the ride without waiting.
1. The period of the sine function model is given by the formula T = (2π)/ω, where ω is the coefficient of t in the function. In this case, ω = 3π, so we can calculate the period as follows:
T = (2π)/(3π) = 2/3
Interpreting the period in the context of the Ferris wheel operation, it means that the last passenger will complete one full cycle on the Ferris wheel every 2/3 minutes.
2. (a) The duration of the ride is given as 15 minutes. To find how many times the last passenger makes a complete loop on the Ferris wheel, we divide the duration by the period:
Number of loops = Duration/Period = 15/(2/3) = 15 * (3/2) = 22.5
So the last passenger who boarded the ride will make approximately 22.5 complete loops on the Ferris wheel.
(b) The position of that passenger when the ride ends can be found by evaluating the sine function model at the end of the ride, which is at t = 15 minutes:
h = 82.5 sin(3π(15+0.5)) + 97.5
Evaluating this expression will give you the position of the passenger when the ride ends.
3. (a) To find the height of the last passenger at the moment of the power outage, we can evaluate the sine function model when t = 6:
h = 82.5 sin(3π(6+0.5)) + 97.5
Calculating this expression will give you the height of the last passenger at the moment of the power outage.
(b) The last passenger does not need to wait to exit the ride in this scenario because the height at t = 6 is not at its maximum. This means that the cage of the last passenger can be manually cranked to the lowest position without any additional waiting time.
look below at Marie's question and my reply to that
You should be able to answer the rest of these
You also replied in that question, so it should be easy to find