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March 29, 2024, 09:12:37 pm

Author Topic: VCE Specialist 3/4 Question Thread!  (Read 2164619 times)  Share 

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soccerboi

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Re: Specialist 3/4 Question Thread!
« Reply #630 on: August 26, 2012, 06:40:00 pm »
0
An engine of mass 40 tonnes is pulling a truck of mas 8000kg up a plane inclined at theta to the horizontal where sin(theta)=1/8. If the tractive force exerted by the engine is 60000N, calculate blahblahblah

Is there suppose to be frictional force behind the engine and behind the truck? The solutions didn't consider friction but i'm confused as to why?

Thanks
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Re: Specialist 3/4 Question Thread!
« Reply #631 on: August 26, 2012, 06:49:20 pm »
0
Hello, just a quick question:

What exactly are we doing when we resolve vector a in the direction of vector b?

I know how to do it, just not sure why!

YEAH, if someone can explain this, i'd be very happy =)

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Re: Specialist 3/4 Question Thread!
« Reply #632 on: August 26, 2012, 07:07:50 pm »
+1
An engine of mass 40 tonnes is pulling a truck of mas 8000kg up a plane inclined at theta to the horizontal where sin(theta)=1/8. If the tractive force exerted by the engine is 60000N, calculate blahblahblah

Is there suppose to be frictional force behind the engine and behind the truck? The solutions didn't consider friction but i'm confused as to why?

Thanks

Assuming that this is from Essential, it says smooth plane.

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TrueTears

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Re: Specialist 3/4 Question Thread!
« Reply #633 on: August 26, 2012, 07:26:26 pm »
+2
Hello, just a quick question:

What exactly are we doing when we resolve vector a in the direction of vector b?

I know how to do it, just not sure why!
If you want a kind of intuitive explanation, technically we call it a vector "projection", this name makes more sense as it is essentially just "projecting" the vector's tail onto the other vector and finding an expression for that vector, see diagram: http://en.wikipedia.org/wiki/File:Projection_and_rejection.png, note that a_1 is the "projection" formed.

It is very useful in many applications (especially in linear algebra) because we are often interested in the shapes that are formed when things in 3D space are "projected" onto a 2D plane (ie, shadows from buildings etc). The more technical (and general) definition of vector projections are found here: http://en.wikipedia.org/wiki/Vector_projection#Generalizations
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Re: Specialist 3/4 Question Thread!
« Reply #634 on: August 26, 2012, 09:06:13 pm »
0
An engine of mass 40 tonnes is pulling a truck of mas 8000kg up a plane inclined at theta to the horizontal where sin(theta)=1/8. If the tractive force exerted by the engine is 60000N, calculate blahblahblah

Is there suppose to be frictional force behind the engine and behind the truck? The solutions didn't consider friction but i'm confused as to why?

Thanks

Assuming that this is from Essential, it says smooth plane.
Yeah its from essentials, but i don't see the word "smooth" anywhere in the question.
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Re: Specialist 3/4 Question Thread!
« Reply #635 on: August 27, 2012, 03:34:49 pm »
0
Here's one thats bugging me:

a = sin(t)i+cos(t)j
b = cos(t)i + j

Determine when a and b are at right-angles.

Therefore, I used the dot product and came to this step:

sin(t)cos(t)+cos(t)=0,

and I thought we'd divide both sides by cos and solve for sin, yet, when I look at the answers it does this:
i) cos(t)(sin(t)+1))=0, solving cos(t) =0 and sin(t)+1=0

Is there a reason they've factorised and solved seperately?

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Re: Specialist 3/4 Question Thread!
« Reply #636 on: August 27, 2012, 04:05:38 pm »
+1
If you divide by then you'll be losing solutions (i.e. the solutions for , hence why they factored the out and then used the null factor law, then solved seperately, as it keeps these solutions.
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Re: Specialist 3/4 Question Thread!
« Reply #637 on: August 27, 2012, 04:07:19 pm »
+1
Here's one thats bugging me:

a = sin(t)i+cos(t)j
b = cos(t)i + j

Determine when a and b are at right-angles.

Therefore, I used the dot product and came to this step:

sin(t)cos(t)+cos(t)=0,

and I thought we'd divide both sides by cos and solve for sin, yet, when I look at the answers it does this:
i) cos(t)(sin(t)+1))=0, solving cos(t) =0 and sin(t)+1=0

Is there a reason they've factorised and solved seperately?
The reason you need to factorise it out is so that you don't get rid of any possible solutions. For example, if you want to solve then dividing by x will only leave .
Hence, you only end up with and no longer have the solution . Doing this with cos(t) is the same idea.
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Re: Specialist 3/4 Question Thread!
« Reply #638 on: August 27, 2012, 06:54:38 pm »
+4
how can an object be in two places at once? /Y/ to quantum mechanics!
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Re: Specialist 3/4 Question Thread!
« Reply #639 on: August 27, 2012, 07:55:11 pm »
0
This is almost the exact question to Ringwood Secondary's Specialist SAC last year (and I presume, this year too). But yeah, you just combine the two position vectors for each spinning wheel, and make sure you take into account the rotation direction.
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Re: Specialist 3/4 Question Thread!
« Reply #640 on: August 27, 2012, 07:59:31 pm »
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What was the question? ??? :O

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Re: Specialist 3/4 Question Thread!
« Reply #641 on: August 27, 2012, 08:03:56 pm »
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Could of sworn I was reading a thread about a double ferris wheel. Da fuq's wrong with me today? haha my bad
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Re: Specialist 3/4 Question Thread!
« Reply #642 on: August 27, 2012, 08:04:41 pm »
+1
Hmm, I think it was deleted actually, nothing wrong with you haha

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Re: Specialist 3/4 Question Thread!
« Reply #643 on: August 27, 2012, 08:25:24 pm »
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if sin(x) = 1-a/1+a,0<x<pi/2 express cos(2x) in terms of a
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Re: Specialist 3/4 Question Thread!
« Reply #644 on: August 27, 2012, 08:59:13 pm »
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if sin(x) = 1-a/1+a,0<x<pi/2 express cos(2x) in terms of a

use double angle formula