ΘTheta
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Hi guys needs help on this q please,

A ship S is moving with constant velocity (2i-3j)kmh-1 and a ship r with constant velocity 6ikmh-1
a. find the bearing along which S is moving. Answer is 146 degrees
At noon S ia t the point with position vector 8ikm, and Ri is at O (origin which is oi+oj) At time t hours after noon, the position vectors id S and R are skm and rkm respectively.
b. Find s and r in terms of t, Answer is s=i(8+2t) -3tj and r=6ti
At time T hours, R is ue north-east of S, Find the value of T?
I'm stuck at this part and don''t know here to start. Help guys! =) Thanks
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ghostwalker
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(Original post by ΘTheta)
...
IF R is north-east of S, then the vector sr will be parallel to i+j.

So, work out the vector sr to start.

In this case "parallel" simplifies to, the coefficient of the j component will equal the coefficient of the i component.
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ΘTheta
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(Original post by ghostwalker)
IF R is north-east of S, then the vector sr will be parallel to i+j.

So, work out the vector sr to start.

In this case "parallel" simplifies to, the coefficient of the j component will equal the coefficient of the i component.
So SR= i(4t-8)+3jt, and sine it is parallel to i+j,
i(4t-8)+3jt=u(i+j), where u is scalar
so 4t-8=u and 3t=u
4t-8=3t
t=8

If the question said R is south-west of S, would RS be parallel to -i-j? Thanks!
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ghostwalker
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(Original post by ΘTheta)
So SR= i(4t-8)+3jt, and sine it is parallel to i+j,
i(4t-8)+3jt=u(i+j), where u is scalar
so 4t-8=u and 3t=u
4t-8=3t
t=8

If the question said R is south-west of S, would RS be parallel to -i-j? Thanks!
Ish.

If you plot it. R is south-west of S, then RS (i.e. from R to S) runs North-East, and is parallel to i+j.

SR which runs from S to R, is going South-West, and is parallel to -i-j.

Though, of course i+j is parallel to -i-j, so you will get the same result either way.
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ΘTheta
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(Original post by ghostwalker)
Ish.

If you plot it. R is south-west of S, then RS (i.e. from R to S) runs North-East, and is parallel to i+j.

SR which runs from S to R, is going South-West, and is parallel to -i-j.

Though, of course i+j is parallel to -i-j, so you will get the same result either way.
I see. So if the question said RS, then you could use i+j, and if it said from SR, then you could use -i-j, and you would get the same answer either way?
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ghostwalker
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(Original post by ΘTheta)
I see. So if the question said RS, then you could use i+j, and if it said from SR, then you could use -i-j, and you would get the same answer either way?
If you had worked out rs, then use a parallel vector in the directon rs, which in this new case is i+j.

If you had worked out sr, the use a parallel vector in the direction sr, which in this new case is -i-j.

They will both give the same result.

And if you choose the "wrong" one, it won't make any difference, other than show you're not understanding the process.

The important thing is the ralationship between the i and the j component, and it's 1:1, whether you use i+j, or -i-j.
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ΘTheta
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(Original post by ghostwalker)
If you had worked out rs, then use a parallel vector in the directon rs, which in this new case is i+j.

If you had worked out sr, the use a parallel vector in the direction sr, which in this new case is -i-j.

They will both give the same result.

And if you choose the "wrong" one, it won't make any difference, other than show you're not understanding the process.

The important thing is the ralationship between the i and the j component, and it's 1:1, whether you use i+j, or -i-j.
If the question said east-south , you would use i-j? Right?
Thanks
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ghostwalker
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(Original post by ΘTheta)
If the question said east-south , you would use i-j? Right?
Thanks
It's South-East, and yes, that would be i-j.
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ΘTheta
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(Original post by ghostwalker)
It's South-East, and yes, that would be i-j.
Thanks for your help. 1 last question, say if the question said that R is 60 degrees relative to the i direction, of S. How would you go about doing that question?
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ghostwalker
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(Original post by ΘTheta)
Thanks for your help. 1 last question, say if the question said that R is 60 degrees relative to the i direction, of S. How would you go about doing that question?
Draw a right-angled triangle. For one unit in the i direction, how many in the j direction, and there's your vector for the direction.

Note, your statement is ambiguous as there are two directions, one roughly North-East, and one roughly South-East, and the question will tell you which one is appropriate.
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ΘTheta
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(Original post by ghostwalker)
Draw a right-angled triangle. For one unit in the i direction, how many in the j direction, and there's your vector for the direction.

Note, your statement is ambiguous as there are two directions, one roughly North-East, and one roughly South-East, and the question will tell you which one is appropriate.
if it was with the north-east version, would is it parallel to i+(sqrt3) j?
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ghostwalker
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(Original post by ΘTheta)
if it was with the north-east version, would is it parallel to i+(sqrt3) j?
Yep.
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