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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: perfectscore on August 12, 2008, 07:36:10 pm

Title: Ferris wheel
Post by: perfectscore on August 12, 2008, 07:36:10 pm: Just a few questions. How do you do part bi and part c? Ive done the rest.
Also, for part d; what does it mean by ' take the new period into account'
and for part e; when you exchange it to anticlockwise; do you just change the negative signs?

(http://i35.tinypic.com/dep6pu.jpg)
(http://i35.tinypic.com/5bp82q.jpg)

Thanks heaps!
Title: Re: Ferris wheel
Post by: Mao on August 12, 2008, 08:19:40 pm: b) i) $\mbox{period}=\frac{2\pi}{n}\implies n=\frac{2\pi}{60}=\frac{\pi}{30}$

ii) D relative to B: $r_2(t)=5\sin\left(\frac{\pi}{30}t\right)i+-5\cos\left(\frac{\pi}{30}t\right)j$

we also know that for B relative to O: $r_1(t)=24\sin\left(\frac{\pi}{150}t\right)i+\left(35-24\cos\left(\frac{\pi}{150}t\right)\right)j$

c) $W(t)=r_1(t)+r_2(t)$ cbf'd writing it all out

d) the period of r1 is 300, whereas the period of r2 is 60. so the new period would be the LCM of these two, i.e. 300.

e) since the ferris wheels rotate at constant speed [i hope], the two $n$ s can be considered as angular velocities. if we rotate counter-clockwise, we would simply make the angular velocity negative of what it was, hence all the arguments inside the trig functions would now be negative.
Title: Re: Ferris wheel
Post by: perfectscore on August 12, 2008, 08:39:59 pm: what do you mean by this: "hence all the arguments inside the trig functions would now be negative."
Title: Re: Ferris wheel
Post by: Mao on August 12, 2008, 08:41:42 pm: sin (x)
Title: Re: Ferris wheel
Post by: perfectscore on August 12, 2008, 08:43:04 pm: do the cos's become negative also?
Title: Re: Ferris wheel
Post by: Mao on August 12, 2008, 08:43:45 pm: $\cos(-\theta)=\cos(\theta)$
Title: Re: Ferris wheel
Post by: perfectscore on August 12, 2008, 08:46:06 pm: so only the sin's change sign
Title: Re: Ferris wheel
Post by: Mao on August 12, 2008, 09:33:58 pm: by request:
$W(-t)=r_1(-t)+r_2(-t)=\left[-5\sin\left(\frac{\pi}{30}t\right)-24\sin\left(\frac{\pi}{150}t\right)\right]i+ \left[35-24\cos\left(\frac{\pi}{150}t\right)-5\cos\left(\frac{\pi}{30}t\right)\right]j$
Title: Re: Ferris wheel
Post by: /0 on August 12, 2008, 09:39:57 pm: I hope this isn't your 'big application sac'...
Title: Re: Ferris wheel
Post by: perfectscore on August 12, 2008, 09:47:21 pm: Quote from: DivideBy0 on August 12, 2008, 09:39:57 pm
I hope this isn't your 'big application sac'...
no; thats soon