Comments on: Relative Velocity – SOS (Save Our Sailormoons!) http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Sun, 05 Feb 2012 17:08:39 +0000 hourly 1 By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-713 Miss Loi Sat, 25 Aug 2007 16:23:06 +0000 http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-713 Kumusta na pinoy? :) Think most readers like the pic more than the question. Oh well ... P.S. Does the grass here really looks greener from your end? Kumusta na pinoy? :)

Think most readers like the pic more than the question. Oh well ...

P.S. Does the grass here really looks greener from your end?

]]> By: AnitoKid http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-712 AnitoKid Sat, 25 Aug 2007 15:26:26 +0000 http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-712 I may not know how to solve the problem, but let me tell you this: I totally enjoyed the post. And loved the pic too! And I kid you not! Got here via EastCoast's site. I totally adore the grass design below! Cool! AnitoKid at www.anitokid.blogspot.com I may not know how to solve the problem, but let me tell you this: I totally enjoyed the post. And loved the pic too! And I kid you not!

Got here via EastCoast's site. I totally adore the grass design below! Cool!

AnitoKid at http://www.anitokid.blogspot.com

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-702 Miss Loi Wed, 22 Aug 2007 05:43:49 +0000 http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-702 Oh Kev, this is not a topic on approximation! Tsk. Instead of assumptions, 'midpoints', 'anywheres', and tediously working backwards, lets talk a bit on <em>position vectors</em>: You must first understand that both ships lie in the same coordinate plane i.e. <var class="vector">i</var>-<var class="vector">j</var> plane. And do you agree that when the ships meet, at time <var>t</var>, their position coordinates (represented by their respective position vectors) are <em>exactly the same</em>? Let <var>B</var> denote the HMS Buddha Foot and <var>F</var> denote the supply ship, i.e. <m>vec{OB}</m> + <var class="vector">v</var><sub>B</sub><var>t</var> = <m>vec{OF}</m> + <var class="vector">v</var><sub>F</sub><var>t</var> which leads to [pmath](matrix{2}{1}{1 12}) + (matrix{2}{1}{30 20})t = (matrix{2}{1}{85 5}) + (matrix{2}{1}{{-50} k})t[/pmath] So can you form the two equations and get your <var>k</var> from here? :) P.S. Understood your reasoning about the time taken. Yeah one ship could reach the point first and <em>waits</em> for the other. But but but ... perfect timing is of the essence! The pirates are really active in these areas and we wouldn't want our <i>kawaii</i> stewardess to be abducted while the ship is stuck waiting in the high seas! Oh Kev, this is not a topic on approximation! Tsk.

Instead of assumptions, 'midpoints', 'anywheres', and tediously working backwards, lets talk a bit on position vectors:

You must first understand that both ships lie in the same coordinate plane i.e. i-j plane.

And do you agree that when the ships meet, at time t, their position coordinates (represented by their respective position vectors) are exactly the same?

Let B denote the HMS Buddha Foot and F denote the supply ship,

i.e.

vec{OB} + vBt = vec{OF} + vFt

which leads to

(matrix{2}{1}{1 12}) + (matrix{2}{1}{30 20})t = (matrix{2}{1}{85 5}) + (matrix{2}{1}{{-50} k})t

So can you form the two equations and get your k from here? :)

P.S. Understood your reasoning about the time taken. Yeah one ship could reach the point first and waits for the other.

But but but ... perfect timing is of the essence! The pirates are really active in these areas and we wouldn't want our kawaii stewardess to be abducted while the ship is stuck waiting in the high seas!

]]> By: Kev http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-698 Kev Tue, 21 Aug 2007 12:14:07 +0000 http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-698 heya! LOL... the sailormoons sure is kawaii neh! Like I say lor.. 11 years never touch A-maths.. all return to teacher liao.. so m using my monkey sense to work this thru... and to answer ur PS, of cos both ships can meet at different times I think. Both ships travel on different velocities would justify meeting at different timing relative to their own starting time. Ok.. here goes my monkey working.. ur ship is at i, 12j and travelling at 30i + 20j km/h, so after an hour will be at coordinate 31i, 32j. Similarly fuel ship will be at coordinate 35i, (5+k)j after an hour. So, assuming they will meet at coodrinate 33i which is the midpoint (don't think my assumption is true; in fact, they can meet anywhere btw 31i and 35i I think depending on their speed.) Assuming they meet at 33i, from 31i to 33i, ur ship needs to travel another 2i. 30i + 20j km/h = 2i+1.33j km/4min. So, ur ship will be at coordinate 33i + 33.33j after 1hr 4 min. For the fuel ship, from 35i to 33i, it needs to travel 2i as well. -50i+kj km/h = -2i+(k/25) km/2.4min. So fuel ship will be at 33i, (5+k+[k/25])j after 1hr 2.4min. since both have to meet, (5+k+[k/25]) = 33.33 (k+[k/25]) = 28.33 (26k/25) = 28.33 so k = 27.24 Hmm.. I work backwards using k=27.24, and both ships will meet each other at coordinate 33i, 33.33j. And it seems possible to me that both ships at different speed will take different amount of travelling time to meet each other. Again these are just my monkey calculations... fire away Miss Loi! =) heya! LOL... the sailormoons sure is kawaii neh! Like I say lor.. 11 years never touch A-maths.. all return to teacher liao.. so m using my monkey sense to work this thru... and to answer ur PS, of cos both ships can meet at different times I think. Both ships travel on different velocities would justify meeting at different timing relative to their own starting time.

Ok.. here goes my monkey working..
ur ship is at i, 12j and travelling at 30i + 20j km/h, so after an hour will be at coordinate 31i, 32j. Similarly fuel ship will be at coordinate 35i, (5+k)j after an hour. So, assuming they will meet at coodrinate 33i which is the midpoint (don't think my assumption is true; in fact, they can meet anywhere btw 31i and 35i I think depending on their speed.)

Assuming they meet at 33i, from 31i to 33i, ur ship needs to travel another 2i. 30i + 20j km/h = 2i+1.33j km/4min. So, ur ship will be at coordinate 33i + 33.33j after 1hr 4 min.

For the fuel ship, from 35i to 33i, it needs to travel 2i as well. -50i+kj km/h = -2i+(k/25) km/2.4min. So fuel ship will be at 33i, (5+k+[k/25])j after 1hr 2.4min.

since both have to meet, (5+k+[k/25]) = 33.33
(k+[k/25]) = 28.33
(26k/25) = 28.33 so
k = 27.24

Hmm.. I work backwards using k=27.24, and both ships will meet each other at coordinate 33i, 33.33j. And it seems possible to me that both ships at different speed will take different amount of travelling time to meet each other.

Again these are just my monkey calculations... fire away Miss Loi! =)

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-697 Miss Loi Tue, 21 Aug 2007 09:52:38 +0000 http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-697 Kev, your answer is very, very close but not quite right! Need to see your workings to know where you started to go off-track. You'll only need very basic <em>column vectors</em> knowledge and <strong>two</strong> equations to solve this. But most importantly, don't get distracted by the <i>kawaii</i> stewardess! P.S. If both ships set off at the same moment, how can they 'meet' at different times??? Kev, your answer is very, very close but not quite right! Need to see your workings to know where you started to go off-track.

You'll only need very basic column vectors knowledge and two equations to solve this.

But most importantly, don't get distracted by the kawaii stewardess!

P.S. If both ships set off at the same moment, how can they 'meet' at different times???

]]> By: Kev http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-696 Kev Tue, 21 Aug 2007 07:51:00 +0000 http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-696 It has been 11 years since I touched A Maths!! Really forgotten what vector calculations are.. but based on my calculations, k = 27 and 19/78 or 27.24 in decimal?? LOL... my answer really look strange.. think sure will fail A-Maths if I take it now.. lol.. btw, I also calculated that ur ship should meet the refuelling ship after travelling 1hr4min, while the refueling one need to travel 1hr2.4min before seeing your? LOL.... Gosh.. I daren't look at weather I'm right or not.. It has been 11 years since I touched A Maths!! Really forgotten what vector calculations are.. but based on my calculations, k = 27 and 19/78 or 27.24 in decimal?? LOL... my answer really look strange.. think sure will fail A-Maths if I take it now.. lol..

btw, I also calculated that ur ship should meet the refuelling ship after travelling 1hr4min, while the refueling one need to travel 1hr2.4min before seeing your? LOL.... Gosh.. I daren't look at weather I'm right or not..

]]> By: kiroii http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-693 kiroii Mon, 20 Aug 2007 15:10:39 +0000 http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-693 yea well thats what i was telling my teacher-.- he merely said tat it would be left as a low priority chapter and there's hardly any point if we dwell too much into this and most a-maths questions are around 5marks so 7 is no biggie? thats what my teacher zee corpulent pygmy says anyway(ps his nt a fat shortie jus a metaphorical joke) yea well thats what i was telling my teacher-.- he merely said tat it would be left as a low priority chapter and there's hardly any point if we dwell too much into this and most a-maths questions are around 5marks so 7 is no biggie? thats what my teacher zee corpulent pygmy says anyway(ps his nt a fat shortie jus a metaphorical joke)

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-692 Miss Loi Mon, 20 Aug 2007 14:38:40 +0000 http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-692 Yes there's no denying that relative velocity can strike fear into the hearts of some but for sure at least one question of its kind will appear in your exam (for this year's syllabus). Moreover they will appear in one of the compulsory questions (i.e. not those either/or kind). It's fine if you skip this during the exam to do other questions first. But if your school skips teaching this topic entirely doesn't it mean you'll be deprived of the chance to score 7 marks from this? Yes there's no denying that relative velocity can strike fear into the hearts of some but for sure at least one question of its kind will appear in your exam (for this year's syllabus).

Moreover they will appear in one of the compulsory questions (i.e. not those either/or kind).

It's fine if you skip this during the exam to do other questions first. But if your school skips teaching this topic entirely doesn't it mean you'll be deprived of the chance to score 7 marks from this?

]]> By: kiroii http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-691 kiroii Mon, 20 Aug 2007 14:00:32 +0000 http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-691 btw miss loi hmm i jus wanna get your comments since my teacher said relative velocity is skipped in some schools as they are difficult to comprehand and should be skipped in the actual exam? btw miss loi hmm i jus wanna get your comments since my teacher said relative velocity is skipped in some schools as they are difficult to comprehand and should be skipped in the actual exam?

]]> By: winston http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-685 winston Sat, 18 Aug 2007 18:10:16 +0000 http://www.exampaper.com.sg/questions/a-maths/relative-velocity-sos-save-our-sailormoons#comment-685 Hello Miss loi, hope you can fave my blog on technorati. Hope this SOS won't be shared with a Nigerian banker ;p Hello Miss loi, hope you can fave my blog on technorati.

Hope this SOS won't be shared with a Nigerian banker ;p

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