VCE Specialist 3/4 Question Thread!

[casbanjo]

Can somebody please help me with part C) of this question. I can find sin(x) but that's all I've got. Thanks

[Zealous]

Why is the vertical component of speed (15 sin (30 ) an opposite sign to the displacement and the acceleration?

I took downwards as positive,

Thus I had s = 5m

a = g m
u= 7.5ms-1
BUT assessors' report had u = -7.5m

So why is the vertical component acting in an opposite direction to the rest? Someone explain? I thought it would be pulling the skiier downwards so it's the same direction as acceleration?

They've defined downwards as positive. The vertical component of the velocity is working upwards as soon as the waterskier leaves the ramp, and it is the acceleration of gravity which will work against the velocity in the opposite direction pulling the skier downwards - not the velocity itself.  The acceleration of gravity will work against the skier's upwards motion and bring them down towards the water. The acceleration dictates how the velocity will change.

So eventually, the skiers velocity will be a positive value (downwards) once the acceleration of gravity has worked on it for enough time, but initially at the point where we do our calculations, the velocity is negative (the waterskier is moving upwards) and the acceleration of gravity and displacement are positive.

If it's confusing looking it like this, I would suggest defining upwards as positive because that can make a little more sense. Hopefully my wonky explanation makes sense.

Can somebody please help me with part C) of this question. I can find sin(x) but that's all I've got. Thanks

The area of a triangle can be calculated as:

where a and b are the magnitude of two adjacent sides while A is the angle in between them. I think you learn the formula back in General Maths Advanced.

[casbanjo]

The area of a triangle can be calculated as:

where a and b are the magnitude of two adjacent sides while A is the angle in between them. I think you learn the formula back in General Maths Advanced.

Oh, that's on the formula sheet. Ooops.  Thanks though!

[Mieow]

Can someone please help me with this:

[liamh96]

Hi all,

How would one integrate the following:
(2x +3)/(4x^2 + 1)

Thanks in advance
Liam


EDIT:
Don't worry - solved it! just split the numerator up and take it from there.

[psyxwar]

Hey guys:

Likelihood of vector proofs (eg. proof ABCD is a rhombus) on spec exams? If so, exam 1 or 2?

Also, do examiners tend to know different properties of shapes?

For instance, I was doing a question today that needed me to use vectors to prove ABCD is a parallelogram..

I had two options (from my notes).

a) Prove one pair of sides are parallel, and equal in length

b) Prove both pairs are parallel

I chose option a because it's easier but I was reluctant to do it because I don't think (sorry if I am wrong) all examiners would know option a. Is it risky choosing less common options to prove vectors?

Cheers

lol i'm sure the examiners will know that that is a proof.

[casbanjo]

Can someone please help me with this:
(Image removed from quote.)

This seems a bit lengthy, but it gets the result. Is there a quicker way to solve this?

[yoyoball]

Can someone also please help me with this question:

Find all solutions of z^4 -2z^2+4=0, z E C in Cartesian form.

I have attached my working out so far but got a bit stuck :/

hi!!! did you manage to work out the question??? im stuck on the exact same one from vcaa 2013 exam 1 (((((

[Valyria]

hi!!! did you manage to work out the question??? im stuck on the exact same one from vcaa 2013 exam 1 (((((

(z^2)^2 - 2z^2 + 4 =0

You can factorise directly from here or if you can't see it; let m=z^2

m^2 - 2m + 4 =0

You can then apply the quadratic formula

[lolalol]

hi! this is from the 2007 vcaa exam 2 (question 4c).

we're given the velocity vector of an aircraft as well as its position vector. then we're asked to calculate the angle from the runway at which it lands. they've used the velocity vector to find the angle (see attached image). just wondering why we use the velocity vector to find the angle and not the position vector? thank you!

[Robert123]

hi! this is from the 2007 vcaa exam 2 (question 4c).

we're given the velocity vector of an aircraft as well as its position vector. then we're asked to calculate the angle m the runway at which it lands. they've used the velocity vector to find the angle (see attached image). just wondering why we use the velocity vector to find the angle and not the position vector? thank you!

Well the velocity vector provides us the direction the aircraft is travelling in so it would thus provide the angle at which it lands
And for why the position vector won't worl, well here's an analogy for it. If you drops ball into a bucket, it would be heading straight done into the ground. If you throw it on from an a couple of meters away so the ball travels in the direction of a projectile motion, they are both going to have the same position vectors on impact however they clearly going to land inside the buckets at different angles.
Does that clarify it for you?

[lolalol]

Well the velocity vector provides us the direction the aircraft is travelling in so it would thus provide the angle at which it lands
And for why the position vector won't worl, well here's an analogy for it. If you drops ball into a bucket, it would be heading straight done into the ground. If you throw it on from an a couple of meters away so the ball travels in the direction of a projectile motion, they are both going to have the same position vectors on impact however they clearly going to land inside the buckets at different angles.
Does that clarify it for you?

Perfect analogy - I get it now! Thanks so much!

[Valyria]

Hey,

Could someone help me with part (b)? I don't know why left hand portion of the 3rd quadrant is the required region.

u = 1/2 + (3^1/2)/2 i

Thanks in advance

[BLACKCATT]

So w=-u
       =-(1/2 + (3^1/2)/2 i)
The angle of this is in the 3rd quadrant (-1/2,-sqrt3/2), Arg(w) = pi/3 which intersects with Arg(z)

[Valyria]

So w=-u
       =-(1/2 + (3^1/2)/2 i)
The angle of this is in the 3rd quadrant (-1/2,-sqrt3/2), Arg(w) = pi/3 which intersects with Arg(z)

So why doesn't this cover the other portion of the 3rd and 4th quadrant?