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HSC 2015 MX2 Marathon (archive) (7 Viewers)

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Kaido

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Re: HSC 2015 4U Marathon

Yeah i got to there, but im not sure where to go lol

should i let u=x-2
then do another trig sub, then reverse everything back
 

InteGrand

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Re: HSC 2015 4U Marathon

Yeah i got to there, but im not sure where to go lol

should i let u=x-2
then do another trig sub, then reverse everything back
Yeah, that's one way, or you can use integration by parts after letting .
 

InteGrand

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Re: HSC 2015 4U Marathon

Actually, trig. sub. should be easier in this case.
 

Drsoccerball

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Re: HSC 2015 4U Marathon

Integrand where the mechanics questions at doe?
 

InteGrand

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Re: HSC 2015 4U Marathon

Here was the integration by parts method:















 

Drsoccerball

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Re: HSC 2015 4U Marathon

He answered the extra challenge Q that I'd given before (which wouldn't be asked in HSC).
Is the answr it takes longer on its way up since its being opposed by two vectors: weight and resistance while on the way down the weight vector is positive therefore quicker on the way down ?
 

InteGrand

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Re: HSC 2015 4U Marathon

Is the answr it takes longer on its way up since its being opposed by two vectors: weight and resistance while on the way down the weight vector is positive therefore quicker on the way down ?
It takes longer on the way down.

And in the HSC, I'm guessing they'd expect you to prove this by finding the time of ascent and time of descent.
 

InteGrand

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Re: HSC 2015 4U Marathon

Is the answr it takes longer on its way up since its being opposed by two vectors: weight and resistance while on the way down the weight vector is positive therefore quicker on the way down ?
Here's braintic's answer:

Extra challenge: As resistance is a non-conservative force (since it is dependent on velocity and not position), only reducing the total energy of the body, at any point in its downward path it must have less kinetic energy and hence less speed than at that point in its upward path (because potential energy is the same at both times). Since it is slower all the way down, it takes longer on the way down.

But you wouldn't need to know this for HSC.
 

Kaido

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Re: HSC 2015 4U Marathon

need help with this:
volume obtained by rotating (x-1)^2+y^2/4=1 about y-axis using slices
 

Drsoccerball

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Re: HSC 2015 4U Marathon

need help with this:
volume obtained by rotating (x-1)^2+y^2/4=1 about y-axis using slices
Since i had troubles with both methods at the beginning ill help yah
So first sketch the circle and draw a line perpendicular to the axis of rotation and it it intercepts twice
In order to find where they intercept you have to make x the subject




 
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Kaido

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Re: HSC 2015 4U Marathon

Ahh i see, i was just confused due to the +/- sign, so the outer radius assumes the larger x value - therefore a + sign?
 
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