anonymous
  • anonymous
Help please!! :( long question! calculus Aunt Norma is riding a Ferris wheel. The Ferris wheel has a radius of 50 feet, and the center of the wheel is 58 feet off the ground. The wheel is spinning counterclockwise with an angular velocity of 0.2 radians per second. Uncle Norm is standing in the plane of the Ferris wheel, 60 feet to the right of the base at a height of 0 feet. How fast is the distance between Aunt Norma and Uncle Norm changing when she is 28 feet off the ground and going up?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
let me see if i have the picture |dw:1332439852517:dw|
anonymous
  • anonymous
yes that's correct!
anonymous
  • anonymous
somehow we have to get a relation between the distance and \[\theta\] maybe need the law of cosines?

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anonymous
  • anonymous
can you explain?
anonymous
  • anonymous
|dw:1332440473882:dw|
anonymous
  • anonymous
my picture was misleading. here is a better one
anonymous
  • anonymous
we know one side of that inner triangle is 50 and the other if 58, maybe we can get an expression for the third side in terms of theta using the law of cosines. i have to think
anonymous
  • anonymous
doesnt the law of cosines only work for right triangles though?
anonymous
  • anonymous
no pythagoras is for right triangles, law of cosines in generalization
anonymous
  • anonymous
okay. how do you solve for it?
anonymous
  • anonymous
well i still didn't get an expression for the distance yet, only know that \[h^2=50^2+58^2-2\times 50\times 58\times \cos(\theta)\] and with that maybe we can find the distance we are looking for
anonymous
  • anonymous
i have to run, but i will try this with pencil and paper later and reply back. you need some sort of relation between the angle and the distance. that is what i am trying to figure out. if you can figure one out then we can solve easily. back later
anonymous
  • anonymous
okay thanks!
anonymous
  • anonymous
how fast... sounds like derivatives to me.
anonymous
  • anonymous
can you help? :(
anonymous
  • anonymous
yes need some relation between theta and the distance
TuringTest
  • TuringTest
are you working with parametric equations by chance?
anonymous
  • anonymous
|dw:1332446019813:dw|
anonymous
  • anonymous
i get \[h^2=58^2+50^2-2\times 58\times 50\cos(\theta)\] but that is not the distance, that is just one side of the triangle. other is 60 and third is the one we want
anonymous
  • anonymous
|dw:1332446569744:dw| \[x^{2} = d^{2} + (60 - y)^{2}\]\[\sin \theta = \frac{y}{50}\]\[d = 58 - 50\sin \theta\] so, \[x^{2} = (58 - 50 \cos \theta)^{2} + (60 - 50\sin \theta)^{2}\] then get\[\frac{dx}{d \theta}\]
anonymous
  • anonymous
uuhh no wait we have to get rather,\[\frac{dx}{dt}\]
TuringTest
  • TuringTest
that looks good @rlsadiz just to point out a we need... yeah you beat me to it but that is okay becaus\[\frac{dx}{dt}=\frac{dx}{d\theta}\frac{d\theta}{dt}\]and \(d\theta/dt\) is given
anonymous
  • anonymous
what was \[d \theta/dt\]?
TuringTest
  • TuringTest
the problem says "...with an angular velocity of 0.2 radians per second." so that is \({d\theta\over dt}\)

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