VCE Specialist 3/4 Question Thread!

[lzxnl]

^ Not sure if I'm answering your actual question, but why not differentiate the expression as a function of t, then sub in t=0?

>
>sub in t=0,
>so A is true, and because t is either 0 or a positive number, acceleration is always negative. (ie. B is true)

Then again, you might have tried it already, and I might have completely missed the gist of your question lol.

You've missed the point of his question. The acceleration is the time derivative of the velocity, and a derivative dy/dx is defined as the limit of (y(x+h)-y(x))/h as h approaches zero. This is all and well, but the limit definition requires the approach from both sides. Therefore, the derivative cannot be defined at an endpoint; the limit from one side will not exist as the function will not exist. Thus, the acceleration is formally undefined at t=0.

[Will T]

From Kilbaha 2011 exam 2

when we want to find 'the angle at which the golf ball strikes the ground' are we measuring anti-clockwise from horizontal i.e. 132.63 degrees or clockwise from the negative horizontal i.e. 47.356 degrees ...... (these numbers are if you sub in V = 49, alpha = 25 degrees, k = 0.2
I thought it would be the obtuse angle but solutions disagree...

[Stevensmay]

General idea is that we want to resolve all our forces into ones that are parallel and perpendicular to the slide/plane.

https://www.dropbox.com/s/2jiq4fr4v9l8v0z/2013-10-20%2022.37.10.jpg

Start with our perpendicular component.



Now we move onto our parallel components, using the equation f = ma.







I'm going to assume there is a sign error in the show that portion of the question.

Part b is straight forward to do now, using our equations for motion with constant acceleration.


Solve with CAS now to speed things up.
We will get two solutions, one negative and one positive.
Discard the negative saying leaves us with seconds.

[random_person]

Hey everyone,

I was just wondering if someone can rank the spesh exams from the past 5 years in terms of difficulty?
I know difficulty is a subjective thing, but roughly...

Cheers guys

[LOLs99]

Can someone please explain Q22 MC : http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010specmath2-w.pdf
 Why have to plus (V(initial))^2? Is this related to numerical integration or something else.

[Stevensmay]

The added term is effectively the constant of integration. Adding it as part of our initial conditions means we do not have to find what + c equals later on, saving time.

It is squared as we integrated with respect to and not v. This is a bad explanation sorry.

[lzxnl]

Hey everyone,

I was just wondering if someone can rank the spesh exams from the past 5 years in terms of difficulty?
I know difficulty is a subjective thing, but roughly...

Cheers guys

I'm not too sure on them, but I would rate 2008 and 2011 exams as being at the bottom. 2011, the cutoff for an A+ for exam 1 was 39/40 (I did that exam in 17 minutes). Exam 2 was normal, at around 90% for A+.

The 2008 exam was the only exam I had ever gotten 100% on during my first go, so I'd have to rank that near the bottom.
But yeah, I don't have very high regard for VCAA spesh exams in general because they take me less time than Methods to do.

[random_person]

Thanks nliu1995

[Will T]

A stone of mass 10 kg is released from rest from the top of a cliff. While falling, the stone experiences a wind resistance force that is proportional to its speed. If the constant of proportionality is 2.5, the time taken for the stone to reach a speed of 20 metres per second, correct to two decimal places is equal to? (TSSM 2013 Exam 2 Q.22)

Herp me.

[Stevensmay]

A stone of mass 10 kg is released from rest from the top of a cliff. While falling, the stone experiences a wind resistance force that is proportional to its speed. If the constant of proportionality is 2.5, the time taken for the stone to reach a speed of 20 metres per second, correct to two decimal places is equal to? (TSSM 2013 Exam 2 Q.22)

So first off we want to identify our knowns and forces. From the question we have
when
which is also and we know , our constant of proportionality. From this we can see that the force of the wind resistance is
We also known that there will be the weight force acting downwards, provided by gravity.

As this isn't constant acceleration we cannot use the relevant formulae, thus we must set up an equation of motion based on F=ma. I'm taking down to be positive.



but we also know

but this is inconsistent so we 'flip' it.



Now we can finally get around to integration.



Enter this on your calculator to get

Substitute in and solve.


which is approximately = 2.86, or 2.85 if you go with TSSM's answer.

[Will T]

As this isn't constant acceleration we cannot use the relevant formulae, thus we must set up an equation of motion based on F=ma. I'm taking down to be positive.

Thanks but, this is where I'm slightly confused.....
essentials pg. 397
they say that a = 0.2v^2 - g for the same type of scenario (except up is positive)
Which would be inconsistent....

[Stevensmay]

Pg 397 for me is different to the question posed. Maybe we have different editions.

[Will T]

10.5 Other expressions for acceleration.

Example 22

An object falls from a hovering helicopter over the ocean 1000 m above the sea level. Find the velocity of the object when it hits the water:
a) neglecting air resistance.

b) assuming air resistance is 0.2v^2.

for b) it says a = -9.8 + 0.2v^2.......
That's what I find inconsistent.

[Stevensmay]

Air resistance is an arbitrary thing, it is not a constant and changes between questions.

Eg in one question I might have a bullet, the other a couch. These will have different surface areas and thus different air resistances.
Mass of the particles can also be different.

[LOLs99]

The added term is effectively the constant of integration. Adding it as part of our initial conditions means we do not have to find what + c equals later on, saving time.

It is squared as we integrated with respect to and not v. This is a bad explanation sorry.

I was thinking of numerical integration where u have to plus initial value but that yeah that makes sense now thanks!