VCE Specialist 3/4 Question Thread!

[Bestie]

thank you!

i have another q?
At what angle from the runway, correct to the nearest tenth of a degree, does the aircraft land?


What distance does the aircraft travel from the time it is observed on the radar screen to the time it lands?
Give your answer correct to the nearest metre.

[psyxwar]

thank you!

i have another q?
At what angle from the runway, correct to the nearest tenth of a degree, does the aircraft land?

too lazy to work this out but:

1) let k component=0, find t value for where this occurs -> this is WHEN it lands
2) v(t1), where t1=time it lands for velocity vector at this point in time
3) velocity vector is in the form ai+bj+ck . plenty of ways of finding the angle, the easiest is to draw a triangle with hypotenuse |v(t1)| and opposite side being the k component of the vector. sin(theta)=opposite/hypotenuse, thus you can find the angle.

[chickenfries]

how is this equal to pi/2?

[psyxwar]

how is this equal to pi?

sine both sides (double angle formula)

[lzxnl]

Differentiate arcsin x + arccos x. You should get 0. That means this function is constant. Sub in x = 0 to get arcsin x + arccos x = pi/2 identically (as it's equal to pi/2 when x=0 and because the derivative is 0, the function is exactly pi/2).

[keltingmeith]

Edit - Here's a graph form: https://www.desmos.com/calculator/yd8n2juo4g, pretty fun to play around with.

You have no idea how many exams I will now fail because I'll be too busy playing with this to study...

[lzxnl]

You have no idea how many exams I will now fail because I'll be too busy playing with this to study...

Given that number ranges from zero to all of them, it's not too hard to work out

[M_BONG]

Given that number ranges from zero to all of them, it's not too hard to work out

Oh my god Nickliu gags trolololol

[Valyria]

Hey,

Just say the question didn't specify whether the answer had to be left in a certain form such as 'aIn(b)' and you left your answer as 2In2 -1/2In4, would you be awarded the final mark?

[Zealous]

hey,

can someone please explain VCAA 2008 Exam 2 MC Q17 (the vector one please)

I got the ratio ie. PQ: QR = 2:1 but don't know what to do after..
http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2008specmaths2-w.pdf

Hope that helps!

[lzxnl]

Hey,

Just say the question didn't specify whether the answer had to be left in a certain form such as 'aIn(b)' and you left your answer as 2In2 -1/2In4, would you be awarded the final mark?

You shouldn't be given the final answer mark there as it's simply ln 2. You're expected to be able to simplify that.

Vector r = OR
OR = OP + PR = OP + PQ + QR (these are vectors)
QR = 1/2 PQ and PQR are on the same line => vector QR = 1/2 vector PQ
OR = OP + PQ +QR = OP + PQ + 1/2 PQ = OP + 3/2 PQ = OP + 3/2 (OQ- OP) = OP - 3/2 OP + 3/2 OQ = 3q/2 - p/2
A

[speedy]

Could someone help with this?

Spoiler

[Zealous]

Could someone help with this?

Spoiler

Just show that A, O and B are collinear (on the same line):



Hence, A, O and B are collinear as they are parallel and share a point in common (A).

[speedy]

Just show that A, O and B are collinear (on the same line):



Hence, A, O and B are collinear as they are parallel and share a point in common (A).

Ohh, so if any vector (AB) is parallel to another vector which passes through the origin (AO) then that vector (AB) must pass through the origin! So simple, but I hadn't seen anything like it before. Thanks!

[Robert123]

Ohh, so if any vector (AB) is parallel to another vector which passes through the origin (AO) then that vector (AB) must pass through the origin! So simple, but I hadn't seen anything like it before. Thanks!

Not all the time, they must share a point in common. Think of it like in methods with infinite solutions and no solutions for a  linear function and the line y=x. In both cases, they are parallel  however only the one with infinite solutions will go through the origin.
Does that clarify it for you?