VCE Specialist 3/4 Question Thread!

[Jeggz]

VCAA Exam 2- 2007
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007specmaths2.pdf
Question 5f)
I got the integral but I don't know how to solve because it's not working on my calculator? :\ And also just in general, when you are required to work out the time in terms of 'T' and the integral is 'dt' how would you go about working that out? Not sure if that makes sense..

[barydos]

"If force ai + bj and ci + dj newtons act simultaneously on an object of m kg, it's acceleration in ms^-2 will be?
If the question wanted us to find the magnitude of the acceleration, would it explicitly say "magnitude of acceleration"? (as the answer to the above question is a vector) Thanks.

Also, for this question, which answer would you choose?

Spoiler

I think they would make it clear. "value" or "magnitude" of acceleration would indicate magnitude. Simply "find the acceleration" -> keep in vector (if it's a vector)

Option D, equilibrium=> netforce = 0, therefore sum of all forces = 0 so T+P+W=0

[ahat]

I think they would make it clear. "value" or "magnitude" of acceleration would indicate magnitude. Simply "find the acceleration" -> keep in vector (if it's a vector)

Option D, equilibrium=> netforce = 0, therefore sum of all forces = 0 so T+P+W=0

If you broke it up into components, so:
0 = (Pcos(30°) - Tsincos(30°))i + (Tsin(30°) + Psin(30°) - W)j, Hence for the i components
0 = cos(30°)(P - T)
T = P
Then could A be correct? Otherwise, what's the flaw in my method?

[barydos]

If you broke it up into components, so:
0 = (Pcos(30°) - Tsin(30°))i + (Tsin(30°) + Psin(30°) - W)j, Hence
0 = cos(30°)(P - T)
T = P
Then could A be correct? Otherwise, what's the flaw in my method?

for your i's , should both be cos, your T is in sin

@M.J.

VCAA Exam 2- 2007
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007specmaths2.pdf
Question 5f)
I got the integral but I don't know how to solve because it's not working on my calculator? :\ And also just in general, when you are required to work out the time in terms of 'T' and the integral is 'dt' how would you go about working that out? Not sure if that makes sense..

uh for 5f)
I did integral 13arcos((13-2t)/7))dt from 3 to 8   PLUS  13arccos(-3/7) * (Tc - = integral of (20-2arctan(t))dt from 0 to Tc
then solved for Tc, it worked for me

um not sure what you mean
but if you have dT/dt = T, flip it dt/dT = 1/t now you can integrate because the rate is dt/dT and your rate is in terms of T so you can integrate dT to get t as the subject

[Jeggz]

for your i's , should both be cos, your T is in sin, and dont the i's cancel out anyway?

@M.J.
uh for 5f)
I did integral 13arcos((13-2t)/7))dt from 3 to 8   PLUS  13arccos(-3/7) * (Tc - = integral of (20-2arctan(t))dt from 0 to Tc
then solved for Tc, it worked for me

um not sure what you mean
but if you have dT/dt = T, flip it dt/dT = 1/t now you can integrate because the rate is dt/dT and your rate is in terms of T so you can integrate dT to get t as the subject

Okaay that makes sense
Thanks mate!

[ahat]

for your i's , should both be cos, your T is in sin

Sorry, mistype My question still holds though, why isn't it A?
I think I see it, because if I did the same thing with the j components then C could be correct too. I think simply, like you said, we just have to do T + P + W = 0. Thanks.

[Alwin]

Sorry, mistype My question still holds though, why isn't it A?

It isn't A because the vectors are not the same, even if their magnitude are the same. So we can't say that T and P (tildes underneath) are the same because they are not pointing in the same direction.

If it had said |T| = |P| or T=P (no tildes) indicating just magnitude, you would be correct

Hope this clears it up for you

[ahat]

It isn't A because the vectors are not the same, even if their magnitude are the same. So we can't say that T and P (tildes underneath) are the same because they are not pointing in the same direction.

If it had said |T| = |P| or T=P (no tildes) indicating just magnitude, you would be correct

Hope this clears it up for you

Riggghhhht! Thank you

[silverpixeli]

hey guys good luck this afternoon, last minite question; does something like 1/x^2 have an asymptote at x=0 if it has a restricted domain of like [3,10) or something? because the asymptote is irrelevant kinda but is it still there? does it could if youre counting how many asymptotes the graph has?

[Chazef]

yeah from the spesh exams I've done I haven't seen any solutions which mark you down for it (:

[zvezda]

Id say you wouldnt need the asymptote. But i could be wrong.
Also, when asked to find the angle at which an object lands on the ground, is it the angle it makes with the positive direction of the vector i?

[Alwin]

Id say you wouldnt need the asymptote. But i could be wrong.
Also, when asked to find the angle at which an object lands on the ground, is it the angle it makes with the positive direction of the vector i?

Not quite. It's the angle between the velocity vector and the x-y plane. I'll find an example for you

here: Re: Specialist Question Thread!

and the other posts around it are a good example

Or, another method if you wanted to work with vectors would be to find the angle it makes with the k unit vector and then subtract it from pi/2, but that takes a bit longer imho

[zvezda]

Sorry i probably shouldve specified my question. Say you have a golf ball that is hit and it moves in the i and j plane. If you were asked "at what angle does the ball strike the ground", would you find the angle the velocity vector makes with the positive direction of i or the negative direction of i?

[Robert123]

Just started 3&4 spec beginning with vectors and my only knowledge about them is from completing 3&4 physics so my understanding of concepts is very weak.
What is the purpose of the dot product of two vectors? I understand why to add vector but I don't understand the purpose of multiplying them.
Could someone explain in very basic terms, thanks

[m.Chemia]

Just started 3&4 spec beginning with vectors and my only knowledge about them is from completing 3&4 physics so my understanding of concepts is very weak.
What is the purpose of the dot product of two vectors? I understand why to add vector but I don't understand the purpose of multiplying them.
Could someone explain in very basic terms, thanks

At VCE level, since you know that a.b=|a||b|cos(θ), where θ is the angle between the two vectors, so if you have the two vectors in their components form (i, j, k), you can then find the angle between them. Also, if one of the vectors, lets say b, is a unit vector, a.b can also be interpreted as the projection of vector a onto the direction b.
You are welcome to PM me you need more specification.