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Mathematics: Post your doubts here!

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well can you please explain to me number 6 (ii) i know the answer and got it right but by complete luck and can't understand how he got it in the marking scheme.

Kay so:
We have Vg/Vb = 2.55 or Vg = 2.55 Vb

First we consider the simplest thing (to consider) aka energy change from X to ground.
Gain in KE = Loss in PE
So 1/2 (m) (Vg square - Vx square) = (m) (g) (H)
Since object starts from rest, Vx is zero.
Thus: 1/2 (m) (2.55Vg square) = (m) (10) (H) (i)
Note that we substitute Vg as 2.55 Vb

Now look at energy change from X to B: (We couldn't care less about energy change from B to ground. I don't in any case. Coz to find H, we need two equations of H and another variable ie Vb)
So we have:
1/2 (m) (Vb square - Vx square) = (m) (g) (H-h)
1/2 (m) (Vb square) = (m) (10) (H - 2.2) (ii) (h = 2.2 we get from prev. ans.)

Substitute... and observe the magic errr get the answer.
 
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Kay so:
We have Vg/Vb = 2.55 or Vg = 2.55 Vb

First we consider the simplest thing (to consider) aka energy change from X to ground.
Gain in KE = Loss in PE
So 1/2 (m) (Vg square - Vx square) = (m) (g) (H)
Since object starts from rest, Vx is zero.
Thus: 1/2 (m) (2.55Vg square) = (m) (10) (H) (i)
Note that we substitute Vg as 2.55 Vb

Now look at energy change from X to B: (We couldn't care less about energy change from B to ground. I don't in any case. Coz to find H, we need two equations of H and another variable ie Vb)
So we have:
1/2 (m) (Vb square - Vx square) = (m) (g) (H-h)
1/2 (m) (Vb square) = (m) (10) (H - 2.2) (ii) (h = 2.2 we get from prev. ans.)

Substitute... and observe the magic errr get the answer.
well this will sound really stupid...probably, why did we use (H-h) and not h immediately aren't i supposed to use the height from the ground to point B?
 
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well this will sound really stupid...probably, why did we use (H-h) and not h immediately aren't i supposed to use the height from the ground to point B?
Sometimes people confuse stupidity with curiosity...
Actually, you can...
Depends on you.

If you follow that route, you'll get:
(m)(g)(h) = 1/2 (m)( (2.55Vb)square - (Vb)square) where 2.55 Vb is Vg
You simplify that to get Vb.
Then you find Vg by putting value of Vb into Vg = 2.55 Vb
Then you simply take energy stuff from H to ground. Put Vg as what you've found.

So yeah... you can do that. Definitely. Didn't think of that. Thanks man ahem Pie-man.
 
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Okay, this is a tricky one.
Screenshot - 5_10_2013 , 9_22_39 PM.jpg

See the picture. The red seats highlight the ones that Mrs. Lin can occupy. She has to sit directly behind a student, so if she occupies those seats then it's possible for a student to be placed in front of her. The reason I kept one seat in the second row uncolored is because one of the seats in the front row is occupied my Mrs. Brown. A student can only take two seats in the front row.
So for Mrs. Lin the possible combinations are 10P1
She can sit behind any of the 5 students, so it's 5P1, the reason you don't count the possible seats for the student is because it doesn't matter where they are placed as long as one of them is in front of Mrs. Lin
Mrs. Brown has to sit in one of the front seats so 3P1
And finally after Mrs. Lin, a student and Mrs. brown has been placed there are 9 remaining passengers and 11 remaining seats. There is no restrictions. So it's 11P9

Total no. of ways = 10P1 * 3P1* 5P1 * 11P9

If all 12 passangers are seated randomly = 14P12
so probability = 10P1 * 3P1* 5P1 * 11P9/ 14P12 =.0687

Hope you get this!
 
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Sometimes people confuse stupidity with curiosity...
Actually, you can...
Depends on you.

If you follow that route, you'll get:
(m)(g)(h) = 1/2 (m)( (2.55Vb)square - (Vb)square) where 2.55 Vb is Vg
You simplify that to get Vb.
Then you find Vg by putting value of Vb into Vg = 2.55 Vb
Then you simply take energy stuff from H to ground. Put Vg as what you've found.

So yeah... you can do that. Definitely. Didn't think of that. Thanks man ahem Pie-man.
oh good then my only mistake was not noticing that Vx is 0 ( hope i don't do these silly mistakes on monday ) :D thanks for the help
 
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i just solved this but only got it on the second trial because at my first try i used 2 sec difference in the equation for SQ but then after checking the marking scheme it was supposed to be used in the equation for SP . (and i don't completely understand why until now) :S

so here is what i did (the correct one):

1- i got the equation for Sp "1/2 x a x (t+2)(squared)"

2- started to get rid of the brackets "1/2 x 1.75 x (t(squared) + 4t +4)
= 0.875(t(squared) + 4t + 4)
= 0.875t(squared) + 3.5t + 3.5

3- got an expression for Sq "1/2 at(squared)"

4- subtracted them from each other to get the distance in-between to be equal to 4.9

0.875t(squared) +3.5t +3.5 - 1/2 x 1.75 x t(squared)
= the "0.875t(squared) is crossed with the "1/2 x 1.75 x t(squared) leaving the equation to be "4.9=3.5t + 3.5"
3.5t=4.9-3.5
t=1.4/3.5 = 0.4

hope you understood what you made wrong and why :)
 
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Hahah i sort ov gt it but why ate we adding 2 to sp and why nt sq as sq was released after p has passed through A and plus why is the initial speed fr p 0 and nt 3.5 ?? :p
 
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Hahah i sort ov gt it but why ate we adding 2 to sp and why nt sq as sq was released after p has passed through A and plus why is the initial speed fr p 0 and nt 3.5 ?? :p
well that part about the 2 at Sp and not in Sq i have no idea exactly, but the initial speed has to be 0 as if you take 3.5 instead you will be getting a different distance than 4.9 which you will then have to deduct the extra distance ... its just to not complicate things, its already complicated as hell why do you want to make it more complicated :D

if you ever find out why the 2 is used in Sp not Sq please tell me....please :D
 
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what are the most challenging exams for paper 4 that i can solve (note i said "that I CAN solve" :p and that had the differentiation and integration rules in them (can't remember name of that part)
 
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This question was done by sum1 else b4, bt i dint get it....
That shit is scary indeed.. I will try to solve it in a couple hours when my mind is out of the dizziness :D
ok guys heres the deal
6 ii 5 students sit anywhere by the window... 5! =120
3 business men sit anywhere= 3!= 6
now for the married couples... there are 2 couples =2 two seats each =2 and 3 seats remaining for each couple =3p2
3p2 *2*2= 24
5!=120
3!=6

24*6*120 = 17280
 
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