Math

posted by .

I have another question I am stuck on that follows a previous question. How do I get an equation for the height of the car on the ferris wheel over a 10 minute period if we start the analysis one minute into the ride.
Can I still use the original formula
h = -35cos(2pi*X/5)+37
I don't understand what part changes to make it one minute into the ride. Appreciate any help, orignal question below.
have a trig question regarding a ferris wheel, radius 35m, axles 37m, clockwise direction, rotates twice every 10 mins. I have calculated the following function:
h = -35cos(2pi*X/5)+37
I have calculated at what height I would be after 3 minutes by substituting X=3 in the above equation. However, I need to calculate at what times I would be 30m off the ground. Can you please tell me if I am on the right track and how to calculate the time?
Many thanks

Maths - Reiny, Tuesday, October 13, 2009 at 8:28am
I agree with your equation, so let' set it equal to 30

30 = -35cos(2pi*X/5)+37
-7 = -35cos(2pi*X/5)
.2 = cos(2pi*X/5)
take the inverse cosine to get
2pi*X/5 = 1.369438
x = 1.09 minutes

check it by repeating the same steps you did finding the height at 3 minutes.

  • Math -

    I am not too sure what you mean by "if we start the analysis one minute into the ride"
    Where do you want the chair to be at 1 minute. The way it is, the chair would be 26.2 m high, (which also confirms my answer of 30 m at 1.09 minutes)
    Do you want the chair to be at a minimum height of 2 m when the time is 1 minute?

    If that is the case, we will have to perform a phase shift on our equation.
    So we want h = 2 at t=1, rather than t=0

    this will do it:

    h = -35cos(2pi/5)(X-1) + 37
    check: remember it takes 5 minutes for one rotation.
    t = 1, h = 2 , at the bottom
    t = 2.25 , h = 37, the height of the axle, check!
    t = 3.5, h = 72 , the height of axle + radius of wheel, check!
    t = 4.75, h = 37 , coming down, height of axle, check!
    t = 6 , h = 2, back at the bottom, check!

    In the original equation, using t values of 0, 1.25, 2.5, 3.75 and 5 will yield the same heights.
    (That is how I checked if your equation was valid)

    BTW, I gave you a time of 1.09 minutes for a height of 30 m.
    That would be on the way up, of course you would reach another height of 30 m on your way down, which would be at (5-1.09) or 3.91 min.
    repeatedly adding 5 minutes to these answers would produce all the times that the chair is 30 m high.

    t =

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. trig question

    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 …
  2. math

    A Ferris wheel with a diameter of 100 feet rotates at a constant rate of 4 revolutions per minute. Let the center of the Ferris wheel be at the origin. The height h (in feet) of a Ferris wheel car located at the point (x, y) is given …
  3. Math-trig

    A Ferris wheel with a diameter of 100 feet rotates at a constant rate of 4 revolutions per minute. Let the center of the Ferris wheel be at the origin. The height h (in feet) of a Ferris wheel car located at the point (x, y) is given …
  4. Pre Calculus 12

    The height h, in metres, above the ground of a car as a ferris wheel rotates can be modelled by the function h(t) = 18cos(πt/80) +19 what is the minimum height of a car?
  5. math

    At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 50 meters and a diameter of 35 meters. It takes the wheel three minutes to make one revolution. If you start your ride at the midline and the …
  6. Math - Trigonometry

    You are riding the ferris wheel at the Montgomery County Fair. The wheel has a diameter of 36 feet and travels at a constant rate of 3 revolutions per minute. A car at its lowest is 4 feet above the ground. Write a sine function to …
  7. Math Help Please I Don't Understand

    A Ferris wheel has a diameter of 60 feet. When you start at the bottom of the Ferris wheel, you are 2 feet from the ground. The Ferris wheel completes one rotation in 2 minutes. Create a function that represents your height relative …
  8. Math

    A Ferris wheel has a diameter of 60 feet. When you start at the bottom of the Ferris wheel, you are 2 feet from the ground.The Ferris wheel completes one rotation in 2 minutes. Create a graph that represents your height relative to …
  9. Advanced Functions

    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 …
  10. math (sinusoidal functions

    The height of the rider on a Ferris Wheel can be modeled by a cosine function. At time t = 0, a rider boards the Ferris Wheel at its minimum height of 3 m. The maximum height of the Ferris Wheel is 39 m. During the 8 minute ride, the …

More Similar Questions