Results 1 to 2 of 2

Math Help - Sinusoidal Word Problem

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    1

    Sinusoidal Word Problem

    A Ferris Wheel has a radius of 12 meters, and the bottom of the wheel passes 3 meters above the ground. At the same time the ride officially begins, Jacky is at some unknown distance from the ground. After 16 seconds, Jacky reaches the highest point on the wheel.

    How would you find the sinusoidal equations? Can anyone explain to me how to do this problem? Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello Salt

    Welcome to Math Help Forum!
    Quote Originally Posted by Salt View Post
    A Ferris Wheel has a radius of 12 meters, and the bottom of the wheel passes 3 meters above the ground. At the same time the ride officially begins, Jacky is at some unknown distance from the ground. After 16 seconds, Jacky reaches the highest point on the wheel.

    How would you find the sinusoidal equations? Can anyone explain to me how to do this problem? Thanks.
    The equation you need will be in the form
    h=a+b\sin(ct+d)
    where
    h is the height above ground in metres
    t is the time in seconds
    a,b,c,d are constants
    You won't be able to solve this completely (you haven't been given enough information) but you can get a set of possible solutions. Here's how:

    \sin\theta takes values between -1 and +1 for all values of \theta, so in the equation above, h takes values from a-b to a+b. Therefore:
    a-b = 3

    a+b= 3+2\times12 = 27
    This gives:
    a=15, b= 12
    When t = 16, h = 27. So plug these values into the equation using the values of a and b that we've just found:
    27 = 15+12\sin(16c+d)

    \Rightarrow \sin(16c+d) = 1

    \Rightarrow 16c+d = 360n+90, for any integer n (This is using degrees - but you can write 2n\pi+\pi/2 in radians if you like)

    \Rightarrow d = 360n+90-16c
    So the equation is of the form
    h = 15+12\sin(ct+360n+90-16c)
    The only other option would be to eliminate c, and express this in terms of n and d. Without more information, that's all you can say.

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig Function Sinusoidal Word Problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 4th 2009, 04:43 PM
  2. Checking sinusoidal function word problems
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: April 26th 2009, 12:47 PM
  3. Sinusoidal function word problems
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: April 26th 2009, 08:46 AM
  4. Sinusoidal Functions-word problem
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 11th 2008, 08:11 PM
  5. trig word problem; sinusoidal function
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 12th 2008, 05:07 PM

Search Tags


/mathhelpforum @mathhelpforum