VCE Specialist 3/4 Question Thread!

[Biceps]

find the cartesian equation for: r(t)=2e^0.3t Cos(2t) i + 2e^0.3t Sin(2t) j
How on earth do you do this??

Then you use formula

That would give the answer in terms of t though not x. wouldn't it?

lol  stupid Jenny

I'm thinking we write 2e^0.3t in term of x and y then equate them

i wouldn't have realised too if i didn't try that earlier

[Jenny_2108]

Did you graph this parametric equation in CAS??? The graph looks like the spiral !!!





This is the parametric equation of Bernoulli's (logarithmic) spiral

Its polar equation 



Anyway, I bet it won't be in Spesh exam so dw about that
Just realise I spend like 2 hrs to figure out wth its and now haven't reviewed anything for Spesh SAC tomorrow LOL. Damn it!!!

[Biceps]

Did you graph this parametric equation in CAS??? The graph looks like the spiral !!!





This is the parametric equation of Bernoulli's (logarithmic) spiral

Its polar equation 

(Image removed from quote.)

Anyway, I bet it won't be in Spesh exam so dw about that
Just realise I spend like 2 hrs to figure out wth its and now haven't reviewed anything for Spesh SAC tomorrow LOL. Damn it!!!

I'm so sorry didn't mean to bother you. Thanks a lot though 

[#1procrastinator]

When you integrate a second order DE twice and you have to make a substitution, why is it wrong to keep the initial substitution and use it for the second integration? So if you subbed in U, how come it's wrong to integrate that U again? And how would you get around this (aside from changing back to x's)

[BubbleWrapMan]

When you integrate a second order DE twice and you have to make a substitution, why is it wrong to keep the initial substitution and use it for the second integration? So if you subbed in U, how come it's wrong to integrate that U again? And how would you get around this (aside from changing back to x's)

Example?

[Jenny_2108]

Did you graph this parametric equation in CAS??? The graph looks like the spiral !!!





This is the parametric equation of Bernoulli's (logarithmic) spiral

Its polar equation 

(Image removed from quote.)

Anyway, I bet it won't be in Spesh exam so dw about that
Just realise I spend like 2 hrs to figure out wth its and now haven't reviewed anything for Spesh SAC tomorrow LOL. Damn it!!!

I'm so sorry didn't mean to bother you.

Nah, you are not. I chose not to study at that day

Anyway, I figure it out
















Sub (1) into








Therefore, the cartesian equation is   

[Biceps]

Did you graph this parametric equation in CAS??? The graph looks like the spiral !!!





This is the parametric equation of Bernoulli's (logarithmic) spiral

Its polar equation 

(Image removed from quote.)

Anyway, I bet it won't be in Spesh exam so dw about that
Just realise I spend like 2 hrs to figure out wth its and now haven't reviewed anything for Spesh SAC tomorrow LOL. Damn it!!!

I'm so sorry didn't mean to bother you.

Nah, you are not. I chose not to study at that day

Anyway, I figure it out
















Sub (1) into








Therefore, the cartesian equation is   

:O wow that is amazing!! you are getting a 50 raw in spesh :O.
Thanks a lot!!

[nisha]

I forgot how to do a question like this.
1. Two objects of equal mass, 1.0kg are connected by a light string slung over a frictionless pulley. They lie on two identical surfaces and are at the point of slipping. Both are situated on a triangle, with Mass 2 slipping, and mass 1 on the surface, directly under a 30 degree angle. Mass 2 is adjacent to a 60 degree angle.
(a) calculate the coefficient of friction for the two surfaces
(b)Mass 2 is now replaced with a mass of 2.0kg. Find the acceleration of the system
(c)Find the magnitude of the tension in the string connecting the two masses
-----------
q2. Two ferries, A and B are travelling at constant velocities, have position and velocity vectors at 10am given by:
r(a)=6i-3j
r(b)=-2i+j
v(a)=-2i+3j
v(b)=2i+j
The distance is measured in km and time in hours.

Show that the ferries collide if they maintain their current velocities and determine the time when this happens.

[Jenny_2108]

I forgot how to do a question like this.
1. Two objects of equal mass, 1.0kg are connected by a light string slung over a frictionless pulley. They lie on two identical surfaces and are at the point of slipping. Both are situated on a triangle, with Mass 2 slipping, and mass 1 on the surface, directly under a 30 degree angle. Mass 2 is adjacent to a 60 degree angle.
(a) calculate the coefficient of friction for the two surfaces
(b)Mass 2 is now replaced with a mass of 2.0kg. Find the acceleration of the system
(c)Find the magnitude of the tension in the string connecting the two masses
-----------
q2. Two ferries, A and B are travelling at constant velocities, have position and velocity vectors at 10am given by:
r(a)=6i-3j
r(b)=-2i+j
v(a)=-2i+3j
v(b)=2i+j
The distance is measured in km and time in hours.

Show that the ferries collide if they maintain their current velocities and determine the time when this happens.

Q1. You need to draw the diagram first. I don't know how to do it here though so its hard to explain
a) You find R₁= ai = (T - g x sin30 - uN₁)i + (N₁ - g x cos30)j
a = T - g sin30 - u x g cos30 (1)
R₂= ai = (T-g x sin60 - uN₂)i + (N₂ - g cos60)j
a = T - g sin60 - u x g cos60 (2)
From (1) and (2), you solve to find u (coefficient friction)

b+c)  Similar as (a), you write again the resultant force of R₂
Then substitute u (you found in (a))and find a and T

Q2) Given velocity => you find r(a) and r(b) by antidifferentiation, then substitite t=10, and r(a),r(b) given to find value of c
They collide when they have the same position at the same time.
After you find r(a) and r(b), you equate them to find t. The same value of t for both is the time they collide

[soccerboi]

Three points, A, B and C, have coordinates A(1, 1, 1), B(2, 3, –6) and C(5, –3, –3),
respectively. If M is the midpoint of AC , use a vector method to show that MB is
perpendicular to AC.

Worked solution
They calculated vectors AB,AC,AM.
Then calculated MB by subtracting AM from AB
Then multiplied AC and MB and it equaled zero.

Im confused about how they got vector MB, can someone explain please?

[Jenny_2108]

Three points, A, B and C, have coordinates A(1, 1, 1), B(2, 3, –6) and C(5, –3, –3),
respectively. If M is the midpoint of AC , use a vector method to show that MB is
perpendicular to AC.

Worked solution
They calculated vectors AB,AC,AM.
Then calculated MB by subtracting AM from AB
Then multiplied AC and MB and it equaled zero.

Im confused about how they got vector MB, can someone explain please?

So you understand they calculate vectors AB, AC, AM yeh?
Then, what they mean is:

Edit: I typed wrong

[soccerboi]

They had MB=AB-AM ? So are they wrong?

[Jenny_2108]

They had MB=AB-AM ? So are they wrong?

They are right. Check my post above again, I typed wrong.

[soccerboi]

Ah ok, thanks jenny

Also, two more questions:

1. Consider the function defined by e^x+y=y+x²+e-1.
Show that y=1 when x=0.
The solutions just subbed (0,1) in and showed that LHS and RHS both equal e.

Does their way answer the question properly? By showing that the LHS=RHS, are they actually showing that y=1 when x=0?

2. Basic question: y=sin^-1(2x).
Whats the domain? i forget how u know when to multiply [-1,1] by 2 and when to divide it by 2

[Jenny_2108]

Ah ok, thanks jenny

Also, two more questions:

1. Consider the function defined by e^x+y=y+x²+e-1.
Show that y=1 when x=0.
The solutions just subbed (0,1) in and showed that LHS and RHS both equal e.

Does their way answer the question properly? By showing that the LHS=RHS, are they actually showing that y=1 when x=0?

2. Basic question: y=sin^-1(2x).
Whats the domain? i forget how u know when to multiply [-1,1] by 2 and when to divide it by 2

1. I think it should be fine or maybe someone else can clarify for you

2. the domain is always within [-1,1] so 2x has to be between -1 and 1
To find domain of x, you divide by 2