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M1 vector question need help!

hi for part b of this question I have no idea why it is solved by using completing the square. I don't get what it means by the minimum speed as time is not given. Why is completing the square used? And finally I don't really get what the question is asking. Thanks in advance.

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Reply 1

Zacken

Original post by coconut64

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You know velocity is

\mathbf{v} = (6t + 1)\mathbf{i} + (3t-5)\mathbf{j}

.

You know that speed is the magnitude of velocity.

You know that the magnitude of a vector

ai + bj

\sqrt{a^2 + b^2}

.

Hence, you know that the speed in this case is

\sqrt{(6t+1)^2 + (3t-5)^2} = \sqrt{45t^2 - 18t + 26}

.

You want to find the minimum value of this expression. You can just find the minimum value of the quadratic

45t^2 - 18t + 26

by finding the turning point and blah blah, then take the square root of that minimum value.

Because the minimum value of the square root of something is the square root of the minimum value of the something.

Reply 2

joostan

Original post by coconut64

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The question wants you to find the minimum speed.
You have the velocity vector. Speed is then the magnitude of this vector, which is as shown in the mark-scheme.

As for the completing the square, one can use that to find the minimum of a quadratic, alternatively as suggested in the mark scheme one can use differentiation.

Reply 3

tiny hobbit

Original post by coconut64

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Can I suggest that you come on here and ask for hints rather than dashing to the mark scheme and deciding that you don't understand it.

Mark schemes do what it says on the tin - they tell the markers what to give marks for. They're not intended to explain how mechanics works.

Reply 4

coconut64

Original post by joostan

Thank you! I finally get it now. I didn't know that they include bit of c2 in there so I have no idea it would be to do with turning points.

Reply 5

coconut64

Original post by Zacken

You know velocity is

\mathbf{v} = (6t + 1)\mathbf{i} + (3t-5)\mathbf{j}

.

You know that speed is the magnitude of velocity.

You know that the magnitude of a vector

ai + bj

\sqrt{a^2 + b^2}

.

Hence, you know that the speed in this case is

\sqrt{(6t+1)^2 + (3t-5)^2} = \sqrt{45t^2 - 18t + 26}

.

You want to find the minimum value of this expression. You can just find the minimum value of the quadratic

45t^2 - 18t + 26

I got the answer now it's just that I didn't know c2 stuff is included in mechanics as well. Do you think this kind of question will come up in the m1 exam in June. One that involves c2 topics? Thanks.

Reply 6

Zacken

Original post by coconut64

It could. You shouldn't categorise your knowledge as "Okay, I'm in my M1 exam, time to pretend I haven't learned any other maths in any other module, all I know is M1." instead you should be open to using any method. The word "minimum" should have got you thinking about calculus right away.

Reply 7

coconut64

Original post by tiny hobbit

Hi, first of all I am sorry if I have offended you but the only reason I posted the markschme is because I don't get why that would be one of the the methods. So this does explain how I can go about solving the question. I don't memorise the markscheme , I learn the method and the markschme clearly says that I can use the method of completing the square or calculus. I don't just upload the markscheme and scream to people that I don't get it. I have thought about this for a while and still have no idea. Also, I am sure everyone who is helping me knows what the answer is. I uploaded the markschme because I want to know how it can be solved in that way. But again, I apologize for any offence I may have caused.

(edited 8 years ago)

Reply 8

tiny hobbit

Original post by coconut64

I wasn't being offended, but I think you would benefit more when you are stuck on a question if you come on here and ask for hints. That way people will usually lead you through the question bit by bit.

Reply 9

Zacken

Original post by coconut64

Hi, first of all I am sorry if I have offended you but the only reason I posted the markschme is because I don't get why that would be one of the the methods. So this does explain how I can go about solving the question. I don't memorise what markscheme , I learn the method and the markschme clearly says that I can use the method of completing the square or calculus. I don't just upload the markscheme and scream to people that I don't get it. I have thought about this for a while and still have no idea. Also, I am sure everyone who is helping me knows what the answer is. I uploaded the markschme because I want to know how it can be solved in that way. But again, I apologize for any offence I may have caused.

You haven't offended her at all (I think), she's simply saying that your first port of call when not understanding a question should be to come and ask on TSR instead of checking the markscheme. I quite agree with this, you'd learn a lot more by asking us first (you get very prompt replies, do you not?) instead of checking and understanding the markscheme. Like you said, we know what the answer is even without proviso of the markscheme and we'd love to be able to prod and poke you in the right direction.

I'm not sure if I'm clearing the matter up properly, so let me give an example:

You see this question, you can't really see what it means or what it's asking or what's going on or what to do and you went off to go and check the markscheme. You didn't understand the markscheme so you went off and asked TSR.

What we're saying is:

You see this question, you can't really see what it means or what it's asking or what's going on or what to do so you should go off and come and ask on TSR without checking the markscheme. We can then help you work through the problem and guide you without you already knowing what the answer is.

Reply 10

Notnek

Original post by coconut64

Which board? For Edexcel M1, only C1 knowledge is assumed so it is pretty unlikely that this question would appear in a real paper.

But you should be able to do this question since a similar thing could come up in a C2 paper.

EDIT: I've realised that in this question you need to minimise a quadratic which can be done without C2 calculus.But I still think it's unlikely to appear.

(edited 8 years ago)

Reply 11

Zacken

Original post by notnek

Which board?

This was an Edexcel Solomon (Paper E) question (7) so your suspensions seem warranted.

Reply 12

tiny hobbit

Original post by notnek

Original post by Zacken

This was an Edexcel Solomon (Paper E) question (7) so your suspensions seem warranted.

Edexcel haven't had one of these questions since the 1990s. I hadn't noticed that they'd gone missing!

Reply 13

Zacken

Original post by tiny hobbit

Edexcel haven't had one of these questions since the 1990s. I hadn't noticed that they'd gone missing!

I like it, it requires some thought on the part of the candidates with regards to using calculus on the entire thing or just on the argument of the square root. Do you think it could make a comeback in recent papers?

Reply 14

tiny hobbit

Original post by Zacken

It used to be a fairly common question. The module then was billed as a paper that didn't require calculus, but it was OK because it could be done by completing the square. Most candidates did use calculus however, particularly if the numbers were a bit unpleasant.