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Expert: - 3/16/2008


Question
a ferris wheel has a radius of 22 feet and has a clearance of 4 feet at the bottom. it is turning clockwise and makes one revolution every 60 seconds. At t=0, you are at the 10 o'clock position. make a sketch of the height above ground as a function of time.
thank you.

Answer

Sine curve
Questioner:   moniclaws
Category:  Advanced Math
Private:  No
 
Subject:  advaced algebra 2/trig
Question:  a ferris wheel has a radius of 22 feet and has a clearance of 4 feet at the bottom. it is turning clockwise and makes one revolution every 60 seconds. At t=0, you are at the 10 o'clock position. make a sketch of the height above ground as a function of time.
thank you.
................................
Hi, Moniclaws,

This is the one that goes up and down, right?  The carousel is the one that goes round and round.

If theta [written @] is the angle made by the radius ending in your seat,
then your height is given by:

y = r sin @ + HC

where r is the radius of the carousel -- oops, ferris wheel, and is 22.
HC is the height of the center = 26 feet. [22 + 4]

y = 22 sin @ + 26

Now what about @ as a function of t?

At t = 0,  @ = 5pi/6.  That is because @ = 0 is your 3-o'clock position and this is 5/12 of 2 pi more rotation.

Since it does 2pi in each minute, that's your 'velocity'.  So

@ = 2pi t + 5pi/6.

Now your function is:

y = 22 sin (2pi t + 5pi/6) + 26

and it should look like the attached picture.

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See also this answer:

http://en.allexperts.com/q/Advanced-Math-1363/2008/3/Sine-cosine-graphs.htm

    Questioner's Rating
    Rating(1-10)Knowledgeability = 10Clarity of Response = 10Politeness = 10
    Commentyou are absolutely BRILLIANT. my teacher has been trying to teach us this concept for nearly a month, with minimal sucess. thanks, again. moniclaws


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Paul Klarreich

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