mechanics 4 relative motion question(s)

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kennz
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Hi there I'm stuck on question 2 part b on the June 2003 m4 paper which is here http://pmt.physicsandmathstutor.com/...%20Edexcel.pdf
and the mark scheme is here http://pmt.physicsandmathstutor.com/...%20Edexcel.pdf

I'm also stuck on this question in the text book, question 12 exercise A which is here
http://pmt.physicsandmathstutor.com/...hapter%201.pdf

They're very similar questions and I just don't understand the logic behind them

thanks
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ghostwalker
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(Original post by kennz)
Hi there I'm stuck on question 2 part b on the June 2003 m4 paper which is here http://pmt.physicsandmathstutor.com/...%20Edexcel.pdf
and the mark scheme is here http://pmt.physicsandmathstutor.com/...%20Edexcel.pdf

I'm also stuck on this question in the text book, question 12 exercise A which is here
http://pmt.physicsandmathstutor.com/...hapter%201.pdf

They're very similar questions and I just don't understand the logic behind them

thanks
Q12A.

This question crops up on here frequently and seems to throw a lot of people.

For the boat to arrive at a distance d downstream, it's resultant velocity must be directly towards that point on the opposite bank, given by the diagonal dotted line - see diagram.


Name:  Untitled.jpg
Views: 99
Size:  27.1 KB

Now, the velocity relative to the bank is u + v. In the diagram, depending on what angle v is at, u + v can lie anywhere on the red circle. There are two possibilities where this circle intersects the diagonal line, and these give you the two possible angles.

Don't be mislead by the fact that one of the v's looks to be at right angles to u, it's just the drawing, it's not a right angle.

June 2003 M4 paper.

Refering to the diagram in this post you can imagine that diagonal dotted line at a different angle, steeper than it currently is. And as you make it steeper, you come to a point where it is tangential to the circle, and this relates to the furthest up the far bank that the boat can aim at.
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kennz
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(Original post by ghostwalker)
Q12A.

This question crops up on here frequently and seems to throw a lot of people.

For the boat to arrive at a distance d downstream, it's resultant velocity must be directly towards that point on the opposite bank, given by the diagonal dotted line - see diagram.


Name:  Untitled.jpg
Views: 99
Size:  27.1 KB

Now, the velocity relative to the bank is u + v. In the diagram, depending on what angle u is at, u + v can lie anywhere on the red circle. There are two possibilities where this circle intersects the diagonal line, and these give you the two possible angles.

Don't be mislead by the fact that one of the v's looks to be at right angles to u, it's just the drawing, it's not a right angle.

June 2003 M4 paper.

Refering to the diagram in this post you can imagine that diagonal dotted line at a different angle, steeper that it currently is. And as you make it steeper, you come to a point where it is tangential to the circle, and this relates to the furthest up the far bank that the boat can aim at.
Awesome, thank you so much. Sound explanation and I can see where the ambiguous case of the sine rule come in here.
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