Edexcel M4 Elastic Collisions (Exercise A Question 11) Watch

Forest10
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Hello All,

I'm revising the Elastic Collisions chapter from the Edexcel text book, and there's a question I'm having difficulty with.

I have attached a copy of the question / answer.
The question is about a collision in the y=x plane (so different to most of the questions in that chapter when collisions occur along the axis).

I have searched for guidance and it seems that this type of question causes some issues for people.

I've kind of reversed engineered an understanding of what is happening by looking at the answer and scrutinising each of the steps but I wonder if someone could answer a couple of questions (note; my questions only relate to part a) of the answer section)

1) Would I be right in thinking that the unit vector of any question of this type would always be 1/sqrt2 because we work off of i+j (although signs might change).

2) When we choose the vectors, for example (-i + j) are we doing this based upon the way the question 'looks' or is there a mathematical way of determining which directions we should take ?

3) Can someone briefly explain what exactly we're doing when we dot the vectors then multiply by the unit vector. (I've tried going over notes from previous mechanics sections and I can't remember that this process gives us).

4) In the final line of the section a) answer; we get the two vectors and then add them; not sure why we do this. I was under the impression they were perp unit vectors so wouldn't we use pythag. Having said that are they adding the vectors to get the resultant vector (which is the velocity vector in this case).

Sorry for the lengthy questions; but once I understand this question I think I'm close to being finished on this chapter.

Thanks
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ghostwalker
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(Original post by Forest10)
1) Would I be right in thinking that the unit vector of any question of this type would always be 1/sqrt2 because we work off of i+j (although signs might change).
I think it unlikely you'd get anything else in an exam, but can't guarantee it.

If you have an equation y=ax, then any point on the line can be represented by the vector x(1,a), so your direction vector for the line is i+aj.

2) When we choose the vectors, for example (-i + j) are we doing this based upon the way the question 'looks' or is there a mathematical way of determining which directions we should take ?
If you have a vector ai+bj, then a perpendicular vector is -bi+aj.

Why? Because (ai+bj).(-bi+aj)=0, hence they are perpendicular.

In this question, a=b=1.

3) Can someone briefly explain what exactly we're doing when we dot the vectors then multiply by the unit vector. (I've tried going over notes from previous mechanics sections and I can't remember that this process gives us).
OK, you're not just dotting two vectors. You're dotting one vector with a unit vector.

(\mathbf{b.\hat{u})\hat{u}} gives you the component of the vector b in the direction of the unit vector u. Similar to when you resolve forces into components, except here it's done in vector form.


4) In the final line of the section a) answer; we get the two vectors and then add them; not sure why we do this. I was under the impression they were perp unit vectors so wouldn't we use pythag. Having said that are they adding the vectors to get the resultant vector (which is the velocity vector in this case).
Yes. You're just adding two vectors to find the final velocity vector.

If they had asked for the speed, then you'd need to take that final velocity vector and apply Pythagoras to the i,j coefficients.
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Forest10
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Thanks for explaining this so clearly; I greatly appreciate your help on this.
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