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Dougggggg
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Homework Statement
I was really struggling with a Calculus problem but I think I have the right answer, this is more just checking with someone than anything.
When given a Ferris Wheel has a radius of 10 m, and that it takes 2 minutes for one rotation, find how fast it is moving from the ground 16 m up.
Homework Equations
x2+y2 = r2
The Attempt at a Solution
I began by taking the derivative of the equation of a circle.
2x [tex]\frac{dx}{dt}[/tex] + 2y [tex]\frac{dy}{dt}[/tex] = 0
sin
Then used some trig to solve for [tex]\frac{dx}{dt}[/tex]
cos[tex]\theta[/tex] = [tex]\frac{1}{r}[/tex]x
I made a triangle with my x and y values in respect to the center of the Ferris Wheel. I also then need to account for my y value being from there and not the ground, so I now use 6 m.
-sin[tex]\theta[/tex] [tex]\frac{d\theta}{dt}[/tex] = [tex]\frac{1}{r}[/tex][tex]\frac{dx}{dt}[/tex]
-rsin[tex]\theta[/tex][tex]\frac{d\theta}{dt}[/tex] = [tex]\frac{dx}{dt}[/tex]
Also, could find [tex]\frac{d\theta}{dt}[/tex] = [tex]\pi[/tex]
Finally solved for [tex]\frac{dy}{dt}[/tex]
x([tex]\pi[/tex]rsin[tex]\theta[/tex])=y[tex]\frac{dy}{dt}[/tex]
[tex]\frac{dy}{dt}[/tex]=8[tex]\pi[/tex]
Yes, no, maybe so?