applied maths

niallofthenine

need help: had a poor teacher for two years, dont want to get into specifics but i need predictions on whats coming up on friday
these are the areas i have prepared/ish
1 projectiles
2 relative velocity
3 accelerated linear motion
4 rigid body rotations
5 impacts and collisions
6 newtons laws and connected articles
thats all. any help/ predictions would be greatly appreciated

Nehpets

Same as me except I'm doing linear motion too. As far as predictions go, I can't help you!

JC 2K3

You can't predict Applied Maths, can you???

In any case, there are great notes on www.skoool.ie , just go to Applied Maths under Senior Cycle.

Nehpets

You know what gets on my nerves? Rel. Velocity.

Anyone have an answer for 1977 rel. vel? On the solutions I have it has 4i + 3j but I'm getting 3i + 4j

JC 2K3

Rel Vel is annoying becuase I can study it and understand it really well, but then get the same mindfúck attempting a question after not looking at it for a while.

I don't have papers going back that far, scan?

Nehpets

I'll just type it up. First part is stupid but ah well:

Explain, with the aid of a diagram, what is meant by the relative velocity of one body with respect to another.

To a cyclist riding North at 7 m/s the wind appears to blow from the North-West. To a pedestrian walking due West at 1 m/s the same wind appears to come from the South-West. Find the magnitude and direction of the velocity of the wind, by expressing it in the form ui + vj or otherwise.

cocoa

+3i+4j here too.

if the pedestrian was walking east their answer would work...i think....

Nehpets

cocoa wrote:

+3i+4j here too.

Grand, I think what they have done wrong in the solutions is that they took the pedestrian walking south (-j) instead of west (-i)

JC 2K3

C = Cyclist
W = Wind
P = Pedestrian

Vc = 7j
Vwc = xi - xj
Vw = xi + (7 - x)j

Vp = -1i
Vwp = yi + yj
Vw = (y - 1)i + yj

(y - 1)i + yj = xi + (7 - x)j
x = y - 1
x = -y + 7
2x = 6
x = 3
y = 7 - 3 = 4

3i + 4j

niallofthenine

nah i think your right!!!

JC 2K3

Perhaps you guys read it as "blowing to" rather than "blowing from" ?

Nehpets

I did this:

Vc = 7j
Vw = ai + bj
Vwc = Vw - Vc
= ai + (b-7)j

Since it's north west: the i = -j
a = -b +7
and therefore b = 7 -a

Then Vwp = Vw - Vp
= ai + bj + i
= (a + 1)i + bj
Since it's southwest: i = j
so b = a + 1

so b = b
a + 1 = 7 - a
a = 3 and b = 4

What did I do wrong?

JC 2K3

You're right, I had a sign wrong, sorry.

EDIT: Edited original post.

Nehpets

See 1991 (Rel Vel again). I've done this:

w = wind
r = runner
c = change in runner

Vw = ai + bj
Vr = ui (given)
Vwr = (a - u)i + bj

Vc = uj (given)
Vwc = ai + (b - u)j

Now you can let i component over j component = -(the apparent direction speed is coming 2i + 3j (this is given)) - I'm just wondering why you do this? and why it's a minus

JC 2K3

Hmmm...

I think they're direction vectors rather than velocity vectors or something?

I'll have to think about this one....

niallofthenine

• The greatest gap between particles P and Q occurs when vp = vq (because if their speeds are unequal then the gap is either increasing or decreasing) can someone explain this to me please! should the = be un=?
confuzzled

Nehpets

niallofthenine wrote:

• The greatest gap between particles P and Q occurs when vp = vq (because if their speeds are unequal then the gap is either increasing or decreasing) can someone explain this to me please! should the = be un=?
confuzzled

What's the question?

ZorbaTehZ

Nehpets wrote:

See 1991 (Rel Vel again). I've done this:

w = wind
r = runner
c = change in runner

Vw = ai + bj
Vr = ui (given)
Vwr = (a - u)i + bj

Vc = uj (given)
Vwc = ai + (b - u)j

Now you can let i component over j component = -(the apparent direction speed is coming 2i + 3j (this is given)) - I'm just wondering why you do this? and why it's a minus

I have a solution to this if you want it?

Like JC said, the reason you let it equal 2/3 and -2/3 is because (direction vectors) it is the ratio of the i component to the j component. The reason you use the negative signs is because you need to differentiate between both - consider if you let both of them equal 2/3, if you did that would be the same as assuming they came from the same direction.

niallofthenine

its in skoool.ie i dont understand how the distance between the particles can be the greatest if the velocities are equal, this would mean that the distance between them is a constant!!

MathsManiac

niallofthenine wrote:

its in skoool.ie i dont understand how the distance between the particles can be the greatest if the velocities are equal, this would mean that the distance between them is a constant!!

...Blood from a turnip. I don't fancy spending an hour or two clicking around on skoool.ie on the off chance of coming across the page you're talking about! Can you give us the text of the question, or a link to it.

[In the absense of the question, let us suppose that you're talking about two objects moving in a straight line. At the instant that their distance from eachother is a local maximum or minimum, their velocities will be equal. If you like, you could think of it in relative-velocity terms. Imagine one of the objects fixed and the other moving relative to it. At the instant the distance is a max, its derivative, the relative velocity, is zero. The relative velocity is the difference of the two velocities, so when it's zero, it means the two velocities are equal.]

Nehpets

ZorbaTehZ wrote:

I have a solution to this if you want it?

Like JC said, the reason you let it equal 2/3 and -2/3 is because (direction vectors) it is the ratio of the i component to the j component. The reason you use the negative signs is because you need to differentiate between both - consider if you let both of them equal 2/3, if you did that would be the same as assuming they came from the same direction.

No need for the solution but thanks. Hmm they both represent the wind relative to the runner so why can't you let i = i and j = j?

ZorbaTehZ

Because when the question says 2i+3j or whatever, its not giving the value of the wind, instead it is giving the direction.
Another way of phrasing the 2i+3j, is to say that the ratio of the i-component of the wind to its j-component is 2:3.

JC 2K3

Ah, so instead of saying "the wind appears to blow from the North West" in a question they could say "the wind appears to blow from the direction -i + j", right?

Nehpets

I see, thanks! In 1998 2 (b) you can do this too, but it's a river question

EDIT: can anyone help with this?

JC 2K3

I didn't use a ratio as such when working it out just there, I took the direction vectors to be unit vectors in the direction of the wind's apparent velocity, ie. the wind's apparent velocity would be the direction vector multiplied by a constant.

So:

Vr = ui
Vwr = 2ai + 3aj
Vw = (2a + u)i + 3aj

Vc = uj
Vwc = -2bi + 3bj
Vw = -2bi + (3b + u)j

-2bi = 2a + u
2a + 2b + u = 0 ....(1)
6a + 6b + 3u = 0 ....(1)*3

3a = 3b + u = 0
3a - 3b - u = 0 ....(1)
6a - 6b - 2u = 0 ....(1)*2

6a + 6b + 3u = 0
6a - 6b - 2u = 0

---

12a = -u
a = -u/12

Vw = (2a + u)i + 3aj
Vw = (-u/6 + u)i - (u/4)j
Vw = (5/6)ui - (u/4)j


EDIT: I see you said "no need for the solution", oh well....

Nehpets

You're way is good/better

Turnip2000

Is every1 doing Q10?? The A part is always a Treat but the B part is just disgusting...every time!:(

And the worst part is the A part only gets like an average of 15 marks??

JC 2K3

You're not serious?? That question is 100% lovely 100% of the time

ZorbaTehZ

Turnip2000 wrote:

Is every1 doing Q10?? The A part is always a Treat but the B part is just disgusting...every time!:(

And the worst part is the A part only gets like an average of 15 marks??

Idd, the part B's are a real bítch sometimes.

Part A's, are almost always worth 20 marks. Part B though, is usually organised so that 75% of the marks are for the first part (i) or both (i) and (ii) if there are 3 parts. Using the example of the 2006 paper, 20 marks went for Part A, 25 for Part B(i) and then only 5 marks for Part B(ii).

ZorbaTehZ

Nehpets wrote:

I see, thanks! In 1998 2 (b) you can do this too, but it's a river question

EDIT: can anyone help with this?

Try and find V(b) in terms of some variable using the distances given. Then try and find V(bc). Draw a diagram in these questions, it usually makes them easier to solve. Solution below if you want it.

Solution:
1998 2 (b)
|V(bc)| = 3.2
|V(b)| = x

Use Pythagoras theorem and you'll find the distance to travel is √2650.
V(b) = 45x/√2650 i + 25x/√2650 j
V(c) = 0i - 3.6j
... V(bc) = 45x/√2650 i + ( 3.6 - 25x/√2650 ) j

Since |V(bc)| = 3.2, root of the sum of the squares.
You get:
x^2 - 36x/√106 + 2.72 = 0

Factor Theorem, and you get:
2.035i + 2.469j and 1.0209i + 3.033j

So direction is E,50.5N and E,71.4N

Feddd

The 05 final part in Q10 was a bitch. Most of them are ok though, just the odd one.


My A team will be Q1, Q2, Q3, Q4, Q5, Q9, Q10. And Q8 as back up if I can't get my 6 out of that list.