HSC Revision Thread 2006 (2 Viewers)

[Riviet]

A revision thread for helping others and preparation for the exam on Wednesday. Feel free to post up questions from anywhere that you're having trouble with.

 

[P_Dilemma]

Can someone post up some SIMPLE explanations on the following:

1. Parametrics
2. S.H.M.
3. Permutations and Combinations.

Thankee!

-P_D

 

[xxPanDa]

what are u guys doin to prepare for tmr?
at night?

i srs duno wah to doo... do a past paper?

 

[zeek]

Past papers past papers past papers = best way to improve right now

if you have the phoenix education practice questions book that goes topic by topic, then i suggest you whip that out and start doing some projectile motion or SHM because that is ALWAYS in questions 5-7.

 

[hjyigkyhok]

I have a S.H.M qu!!!

Assume that the tides rise and fall in S.H.M. A ship needs 10m of water to pass safely. A low tide its 9m deep and at high tide 12m deep. Low tide is @ 9am and high is at 4pm. what time can the ship pass safely.

can anyone show me how??? thx

 

[zeek]

FIRST THING YOU ALWAYS DO IS DRAW A DIAGRAM!!!!!

DIAAAAAAAAAAAGRAAAAAAAAAAAAM

mk

now we know that it takes 7 hours to go from low tide to high tide. Mathematically, this means:

0.5T=7
.: T=14 {but T=2pi/n}
.: n=pi/7 hours

ALSO, we know that the origin of SHM is the average between the amplitudes .: the origin is at 10.5m but we want the origin to be at 0 .: we take away 10.5 from all values.

low tide (-1.5m) origin high tide (1.5m)
++-------------------------0--------------------------++

Next, we start substiuting the values we know into the displacement equation:

x=Acos(nt+e) {A=1.5m, n=pi/7}
.:x=1.5cos(pi.t/7 +e)

We assume that the low tide initially begins when t=0 .: x=-1.5 {Sub these values in to find e}
Now we get the full equation which should be:

x=1.5cos(pi.t/7 + pi)

To find the times when the ship can safely pass, we put in the displacement required which is (10m-10.5) =-0.5

-0.5/1.5=cos(pi.t/7 + pi)
.: we get 2 cases as cos @ is negative in the TAN and SIN quadrants...
0.608=pi.t/7 + pi AND 1.392=pi.t/7 + pi
.:t=-5.645, -3.898 {We add these values to the 4pm, i.e. 1600 hours}
.: t= 12:06 PM, 10:21 AM

Hopefully thats right

 

[hjyigkyhok]

i did something like that...but the answers are : between 11.44am and 8.16pm

 

[zeek]

i think that there might be a problem with the period then

 

[hjyigkyhok]

ahhhhh i cant do it!!! so not ready for tomorrow

 

[zeek]

dw its just one question... study projectiles instead, they're gonna be more harder

 

[B35tY]

How do i show where and when two projectiles collide? Do i find the cartesians of each projectile and solve them simultaneously? Because whenever i try this i get nowhere.

What other *hard* questions can they ask about projectiles?

 

[Naylyn]

One unplesant question that they can ask is getting you to find what angle a projectile must be fired at to land on a raised platform

 

[zeek]

they can ask you to do inequalities with projectile motion... well thats what i've seen, but usually projectile motion tends to be "trickier" than SHM.

How do i show where and when two projectiles collide? Do i find the cartesians of each projectile and solve them simultaneously?

You don't always have to use the cartesian, sometimes it may be easier to use the equations for horizontal and vertical displacement; that is if you have the value for time.

 

[Naylyn]

For the SHM question the equation should be x=1.5cos(pi.t/7 - pi)
Insted of using the point x=-1.5 t=0 to find the values for @ use x=1.5 t=7 then you get
1.5=1.5cos(pi/7 * pi + @)
1=cos(pi + @)
o=pi + @
@= -pi
which gives
x=1.5cos(pi.t/7 - pi)

From there you should get the correct answer if you follow the same working out as above.

 

[bambii]

hmm didnt work out for me like that...

low tide (1.5m) origin high tide (-1.5m)
l-------------------------0--------------------------l
10m begins(0.5m) 10m ends(-0.5m)

a=1.5 n= pi/7 Its already been shown

X= 1.5cos{pi.t/7 + @}
at t=0 x=1.5

1.5=1.5 cos{pi.(o)/7 +@}
1= cos{pi.t/(0) +@}
so @=0

begins x=0.5

1/3=cos{pi.t/7}
t= 2.742...
add 9am ... 10m tide begins 11.44 am

Ends x=-0.5
... same working

8.16pm

 

[Riviet]

What other *hard* questions can they ask about projectiles?

All kinds of random stuff, like inequalities when a projectile just clears a fence, or the range of a projectile that's thrown at a slope. Check out some past HSCs. Many years have a projectile question somewhere around Q6-7.