emma64
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Can anyone help with this question (I’ve added a picture below, it’s N2) , the answer is 15.3 degrees
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emma64
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mqb2766
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(Original post by emma64)
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What are you stuck on?
If you know the position, differentiate to get the velocity (direction of motion).
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dextrous63
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You need to find the arctan of both the position vector and the velocity vector and find the difference between them.
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David Getling
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(Original post by emma64)
Can anyone help with this question (I’ve added a picture below, it’s N2) , the answer is 15.3 degrees
Plug t=2 into the original formula to get the position vector r. Now differentiate wrt t to get a formula for v, into which you also plug t=2. The angle you want is now obtained by using the standard dot product formula cos(θ) = rv/|r||v|
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Sir Cumference
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(Original post by David Getling)
Plug t=2 into the original formula to get the position vector r. Now differentiate wrt t to get a formula for v, into which you also plug t=2. The angle you want is now obtained by using the standard dot product formula cos(θ) = rv/|r||v|
The dot product is not part of the A Level spec anymore.
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(Original post by Sir Cumference)
The dot product is not part of the A Level spec anymore.
Bloody hell!!! That's some real serious dumbing down. I hope most teachers have the good sense to teach it anyway. It's so important that the exam boards ought to be truly ashamed of removing this. So much for making exams more rigorous, especially when I think of some of the stuff they have introduced that is far less useful :rolleyes:.
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Sir Cumference
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(Original post by David Getling)
Bloody hell!!! That's some real serious dumbing down. I hope most teachers have the good sense to teach it anyway. It's so important that the exam boards ought to be truly ashamed of removing this. So much for making exams more rigorous, especially when I think of some of the stuff they have introduced that is far less useful :rolleyes:.
Teachers should be focusing on topics that are on the spec in my opinion. There are lots of very important topics in further maths but they can't all be taught to A Level maths students. The exams have been designed so that the dot product formula is not necessary.

I agree that moving most of C4 vectors to FM was a bit of a strange decision but aside from that I think the increase in difficulty and focus on proof & modelling have been positive overall. They probably had to make a decision to get rid of one of the major topics and it was vectors that got the chop.
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dextrous63
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(Original post by Sir Cumference)
Teachers should be focusing on topics that are on the spec in my opinion. There are lots of very important topics in further maths but they can't all be taught to A Level maths students. The exams have been designed so that the dot product formula is not necessary.

I agree that moving most of C4 vectors to FM was a bit of a strange decision but aside from that I think the increase in difficulty and focus on proof & modelling have been positive overall. They probably had to make a decision to get rid of one of the major topics and it was vectors that got the chop.
It's strange that on the (Edexcel) spec, students are supposed to learn the formula for finding the angle between a vector and an axis (see textbook pages 340-341) but not the general dot product. Personally, when tutoring, I show them the dot product as it's far easier to understand and apply.
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Sir Cumference
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(Original post by dextrous63)
It's strange that on the (Edexcel) spec, students are supposed to learn the formula for finding the angle between a vector and an axis (see textbook pages 340-341) but not the general dot product. Personally, when tutoring, I show them the dot product as it's far easier to understand and apply.
I personally don't think any formula is necessary for that topic. If the student draws the vector then they should be able to see that they can use simple trig to find the angle.
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David Getling
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(Original post by Sir Cumference)
I personally don't think any formula is necessary for that topic. If the student draws the vector then they should be able to see that they can use simple trig to find the angle.
A chainsaw isn't necessary for cutting down a tree, but it's a hell of a lot easier than an ax. Your drawing method is probably more time consuming and error prone. Also, the suggested use of arctan is risky as one of the angles returned might be in the wrong quadrant.

Dot product is the way to go, and Edexcel was very stupid to remove it. But then we've all seen massive screw-ups by money-grabbing Pearson Publishing. My all time favourite was in their own physics book. Part of a large illustration stated that gluons where made up of quarks: doesn't inspire much confidence.
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Sir Cumference
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(Original post by David Getling)
A chainsaw isn't necessary for cutting down a tree, but it's a hell of a lot easier than an ax. Your drawing method is probably more time consuming and error prone. Also, the suggested use of arctan is risky as one of the angles returned might be in the wrong quadrant.

Dot product is the way to go, and Edexcel was very stupid to remove it. But then we've all seen massive screw-ups by money-grabbing Pearson Publishing. My all time favourite was in their own physics book. Part of a large illustration stated that gluons where made up of quarks: doesn't inspire much confidence.
I disagree. Finding the angle between a vector and the horizontal/vertical is something that could be in a GCSE exam - there’s no need to learn a formula. I often find that formulas can distract from what’s going on and if the exam asks a different question to what a student is used to from their textbook then they can apply formulas incorrectly without much understanding.
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(Original post by emma64)
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Where did you get this question from out of interest? Was it from a new spec textbook?
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David Getling
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(Original post by Sir Cumference)
I disagree. Finding the angle between a vector and the horizontal/vertical is something that could be in a GCSE exam - there’s no need to learn a formula. I often find that formulas can distract from what’s going on and if the exam asks a different question to what a student is used to from their textbook then they can apply formulas incorrectly without much understanding.
Neither of the vectors in this question is vertical or horizontal.
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Sir Cumference
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David Getling here is the DFE content for vectors in A Level maths:

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As you can see it's very basic now and doesn't go much further than GCSE and it doesn't mention angles at all. I wouldn't be surprised if the question in the OP is from an old spec textbook.
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David Getling
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(Original post by Sir Cumference)
David Getling here is the DFE content for vectors in A Level maths:

Image

As you can see it's very basic now and doesn't go much further than GCSE and it doesn't mention angles at all. I wouldn't be surprised if the question in the OP is from an old spec textbook.
Fair point. As the new spec hasn't been out long I expect most students need to use questions based on the old one.
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Sir Cumference
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(Original post by David Getling)
Neither of the vectors in this question is vertical or horizontal.
Yes I know, I was responding to dextrous63’s point about the formula given in new spec textbooks to find the angle between a vector and the axes. I should have made this clearer.
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emma64
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(Original post by Sir Cumference)
Where did you get this question from out of interest? Was it from a new spec textbook?
It was on an assignment I was given by my college, so I’m not sure where it came from. Sometimes the questions on our assignments are written by our maths lecturers themselves. Sorry I couldn’t be of more help
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