Login

Welcome, Guest. Please login or register.

March 29, 2024, 02:43:38 am

Author Topic: VCE Specialist 3/4 Question Thread!  (Read 2164270 times)  Share 

0 Members and 5 Guests are viewing this topic.

AlphaZero

  • MOTM: DEC 18
  • Forum Obsessive
  • ***
  • Posts: 352
  • \[\Gamma(z)\Gamma(1-z)=\frac{\pi}{\sin(\pi z)}\]
  • Respect: +160
Re: VCE Specialist 3/4 Question Thread!
« Reply #9525 on: September 06, 2019, 07:55:35 pm »
+1
When should we write a tilda ~ sign under acceleration (for example, F=ma)?
Do we even need the tilda sign at all?
How about for vector calculus and kinematics?

You should write tildes when the particle is moving in 2D or 3D space (ie. when looking at vector functions). Clearly, if you write a tilde for acceleration, you must write one for force too.

We tend to omit it for rectilinear motion since there isn't really a useful notion of 'direction'. The positive and negative directions are determined by the signs of the quantities.
2015\(-\)2017:  VCE
2018\(-\)2021:  Bachelor of Biomedicine and Mathematical Sciences Diploma, University of Melbourne


Tau

  • Trendsetter
  • **
  • Posts: 147
  • Respect: +28
Re: VCE Specialist 3/4 Question Thread!
« Reply #9526 on: September 13, 2019, 09:03:31 pm »
0
When labelling a force diagram, for which components do we need to have tildes?
eg. tension, force, weight, reaction, friction (all of them?)

(apologies if I sound pedantic - I'm trying my best to avoid losing marks for silly mistakes!)

I don’t think you actually need to label them with tildes. You’re actually just specifying  the name for the magnitude, the direction is indicated by the arrow. You can see this in, for example, 2018 Exam 1.
2020 - Bachelor of Science, The University of Melbourne

2019: UMEP Mathematics Extension [First Class Honours (H1)], English [44], Specialist [42 ~ 52], Algorithmics (HESS)
ATAR: 99.50
2018: Physics [46 ~ 48], Methods [41 ~ 46]

undefined

  • Forum Obsessive
  • ***
  • Posts: 323
  • Respect: +19
Re: VCE Specialist 3/4 Question Thread!
« Reply #9527 on: September 25, 2019, 03:10:52 pm »
0
Could someone explain why the force in the vertical direction is 10-8Cos[60] instead of R+10-mg-8Cos[60] for the attached question? Thanks
2018 Methods
2019 English | Chemistry | Economics | Specialist  | Japanese SL

2020 B.Eng/Comm
2021 - 2025 B.CS/Comm Diplang in Japanese @ Monash

jkay__

  • Forum Regular
  • **
  • Posts: 74
  • This is how much I remember: 3.141592653589793238
  • Respect: +29
Re: VCE Specialist 3/4 Question Thread!
« Reply #9528 on: September 25, 2019, 04:02:06 pm »
0
Could someone explain why the force in the vertical direction is 10-8Cos[60] instead of R+10-mg-8Cos[60] for the attached question? Thanks

It's acted upon by the horizontal forces, so it's looking at the body from a bird's eye view. There is therefore no weight force or reaction force to consider in this equation
Secondary Education (VCE)
2018  | Psychology |
2019  | UCAT [87th %ile] | English | Mathematical Methods | Specialist Maths | Accounting | Chemistry |
ATAR | [95.90] |
2020~2023 | BSci (Computing & Software Systems) / Dip. MathSc (Statistics & Stochastic Processes) @ UoM

undefined

  • Forum Obsessive
  • ***
  • Posts: 323
  • Respect: +19
Re: VCE Specialist 3/4 Question Thread!
« Reply #9529 on: September 25, 2019, 04:32:02 pm »
0
It's acted upon by the horizontal forces, so it's looking at the body from a bird's eye view. There is therefore no weight force or reaction force to consider in this equation
Oh, misinterpreted the question. Cheers
2018 Methods
2019 English | Chemistry | Economics | Specialist  | Japanese SL

2020 B.Eng/Comm
2021 - 2025 B.CS/Comm Diplang in Japanese @ Monash

AnonymooseUser

  • Trailblazer
  • *
  • Posts: 30
  • Respect: 0
Re: VCE Specialist 3/4 Question Thread!
« Reply #9530 on: October 05, 2019, 03:59:41 pm »
0
For dynamics questions that want an answer for force in newtons, would you lose marks for including g in the answer?

E.g VCAA Exam 1 2016 Q1c The report gives the answer as 245N but I gave it as 25g

S_R_K

  • MOTM: Feb '21
  • Forum Obsessive
  • ***
  • Posts: 487
  • Respect: +58
Re: VCE Specialist 3/4 Question Thread!
« Reply #9531 on: October 05, 2019, 08:38:50 pm »
0
For dynamics questions that want an answer for force in newtons, would you lose marks for including g in the answer?

E.g VCAA Exam 1 2016 Q1c The report gives the answer as 245N but I gave it as 25g

If you are not required to write the answer "correct to the nearest integer" or something like that, then 25g is fine.

studyingg

  • Trendsetter
  • **
  • Posts: 165
  • Respect: +14
Re: VCE Specialist 3/4 Question Thread!
« Reply #9532 on: October 05, 2019, 09:27:14 pm »
0
Is the magnitude of the vector resolute of a parallel to b equal to the scalar resolute? If this is the case, what about the magnitude of the vector resolute of a perpendicular to b -- is there also a way to link the scalar resolute? Sorry if this is a dumb question...its not explicit in the textbook as far as I can tell.

Tau

  • Trendsetter
  • **
  • Posts: 147
  • Respect: +28
Re: VCE Specialist 3/4 Question Thread!
« Reply #9533 on: October 06, 2019, 12:36:53 am »
+1
Is the magnitude of the vector resolute of a parallel to b equal to the scalar resolute? If this is the case, what about the magnitude of the vector resolute of a perpendicular to b -- is there also a way to link the scalar resolute? Sorry if this is a dumb question...its not explicit in the textbook as far as I can tell.

That’s not a dumb question at all. Yes, the magnitude of the parallel vector resolute is the same as the scalar resolute. Here’s why algebraically:

Scalar resolute \(\mathbf{a\cdot \hat{b}}=\mathbf{\frac{a\cdot {b}}{\| b\|}}\)

and magnitude of parallel vector resolute \(\|(\mathbf{a\cdot \hat{b})\hat b} \|=\frac{\|(\mathbf{a\cdot {b})\hat b} \|}{\| \mathbf{b}\|}=\mathbf{\frac{(a\cdot {b})\|b\|}{\| b\|^2}=\mathbf{\frac{a\cdot {b}}{\| b\|}}}\)

Geometrically, you can consider the scalar resolute as the 'length' of vector a projected along vector b. I can't immediately think of any nice relationship between the length of the perpendicular vector resolute and the scalar resolute. At least other than, by Pythagoras, that \(\mathbf { (a\cdot \hat b)^2+\|a-(a\cdot \hat b)\hat b\|^2= \|a\|^2}\), but that is almost a tautology.
« Last Edit: October 06, 2019, 01:05:02 am by Tau »
2020 - Bachelor of Science, The University of Melbourne

2019: UMEP Mathematics Extension [First Class Honours (H1)], English [44], Specialist [42 ~ 52], Algorithmics (HESS)
ATAR: 99.50
2018: Physics [46 ~ 48], Methods [41 ~ 46]

studyingg

  • Trendsetter
  • **
  • Posts: 165
  • Respect: +14
Re: VCE Specialist 3/4 Question Thread!
« Reply #9534 on: October 06, 2019, 09:23:44 am »
0
That’s not a dumb question at all. Yes, the magnitude of the parallel vector resolute is the same as the scalar resolute. Here’s why algebraically:

Scalar resolute \(\mathbf{a\cdot \hat{b}}=\mathbf{\frac{a\cdot {b}}{\| b\|}}\)

and magnitude of parallel vector resolute \(\|(\mathbf{a\cdot \hat{b})\hat b} \|=\frac{\|(\mathbf{a\cdot {b})\hat b} \|}{\| \mathbf{b}\|}=\mathbf{\frac{(a\cdot {b})\|b\|}{\| b\|^2}=\mathbf{\frac{a\cdot {b}}{\| b\|}}}\)

Geometrically, you can consider the scalar resolute as the 'length' of vector a projected along vector b. I can't immediately think of any nice relationship between the length of the perpendicular vector resolute and the scalar resolute. At least other than, by Pythagoras, that \(\mathbf { (a\cdot \hat b)^2+\|a-(a\cdot \hat b)\hat b\|^2= \|a\|^2}\), but that is almost a tautology.

Makes sense, thanks a lot!!

S_R_K

  • MOTM: Feb '21
  • Forum Obsessive
  • ***
  • Posts: 487
  • Respect: +58
Re: VCE Specialist 3/4 Question Thread!
« Reply #9535 on: October 06, 2019, 09:35:42 am »
+2
Just a minor correction: the magnitude of the scalar resolute = magnitude of the vector resolute. Scalar resolutes can be negative.

This is important in, for instance, 2018 NHT Exam 1, question 2.

cap78

  • Fresh Poster
  • *
  • Posts: 4
  • Respect: 0
Re: VCE Specialist 3/4 Question Thread!
« Reply #9536 on: October 09, 2019, 09:38:45 pm »
+1
Hi, I'm wondering what exam scores are needed to get a 43, 45 and/or 47 study score in Spesh on the final exam. Thanks

studyingg

  • Trendsetter
  • **
  • Posts: 165
  • Respect: +14
Re: VCE Specialist 3/4 Question Thread!
« Reply #9537 on: October 15, 2019, 05:06:24 pm »
0
Just a minor correction: the magnitude of the scalar resolute = magnitude of the vector resolute. Scalar resolutes can be negative.

This is important in, for instance, 2018 NHT Exam 1, question 2.

thank you :)

alanihale

  • Forum Regular
  • **
  • Posts: 53
  • i still haven't taken my L's yet :(
  • Respect: +31
Re: VCE Specialist 3/4 Question Thread!
« Reply #9538 on: October 17, 2019, 09:40:18 am »
0
This is important in, for instance, 2018 NHT Exam 1, question 2.
Speaking of 2018 NHT Exam 1 Question 2,
Could someone please help??
I can't seem to get the value of m no matter how many times I try.
2018 - Further Maths [44]
2019 - English [45] | Spesh [hahaha] | Methods [40] | Chem [41] | Bio [40]
Atar: 98.55

Bachelor of Dental Science (Honours) @ La Trobe

---
'Hard work beats talent when talent fails to work hard'

AlphaZero

  • MOTM: DEC 18
  • Forum Obsessive
  • ***
  • Posts: 352
  • \[\Gamma(z)\Gamma(1-z)=\frac{\pi}{\sin(\pi z)}\]
  • Respect: +160
Re: VCE Specialist 3/4 Question Thread!
« Reply #9539 on: October 17, 2019, 02:36:59 pm »
0
Speaking of 2018 NHT Exam 1 Question 2,
Could someone please help??
I can't seem to get the value of m no matter how many times I try.

The magnitude of the vector resolute of \(\mathbf{a}\) parallel to \(\mathbf{b}\) is given by \[\left|(\mathbf{a}\cdot\hat{\mathbf{b}})\hat{\mathbf{b}}\right|=\left|\frac{\mathbf{a}\cdot\mathbf{b}}{|\mathbf{b}|}\right|,\] since \(|\hat{\mathbf{b}}|=1\). Hence, \[\pm\sqrt{14}=\frac{6+2+3m}{\sqrt{4+1+9}}\ \implies\ 3m+8=\pm 14\ \implies\ m=2,\ \frac{-22}{3}.\]
2015\(-\)2017:  VCE
2018\(-\)2021:  Bachelor of Biomedicine and Mathematical Sciences Diploma, University of Melbourne