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Edexcel M1 - Vectors

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    I'm having problems with this question

    A small boat S, drifting in the sea, is modelled as a particle moving in a straight line at constant speed. When first sighted at 0900, S is at a point with position vector (-2i-4j)km relative to a fixed origin O, where i and j are unit vectors due east and due north respectively. At 0940, S is at the point with position vector (4i-6j)km. At time t hours after 0900, S is at the point with position vector skm.

    a) Calculate the bearing on which S is drifting.
    b) Find an expression for s in terms of t.
    at 1100 a motor boat M leaves O and travels with constant velocity (pi + qj)kmh-1
    c) Given that M intercepts S at 1130, calculate the value of p and the value of q

    I managed to find a) which is 108degrees. For the b) part, don't I need the velocity of S to apply the formula of r=r0+vt? :confused:

    Also, to find c) I need to get the equation at b) first right?
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    (Original post by Akiraryuu)
    I'm having problems with this question

    A small boat S, drifting in the sea, is modelled as a particle moving in a straight line at constant speed. When first sighted at 0900, S is at a point with position vector (-2i-4j)km relative to a fixed origin O, where i and j are unit vectors due east and due north respectively. At 0940, S is at the point with position vector (4i-6j)km. At time t hours after 0900, S is at the point with position vector skm.

    a) Calculate the bearing on which S is drifting.
    b) Find an expression for s in terms of t.
    at 1100 a motor boat M leaves O and travels with constant velocity (pi + qj)kmh-1
    c) Given that M intercepts S at 1130, calculate the value of p and the value of q

    I managed to find a) which is 108degrees. For the b) part, don't I need the velocity of S to apply the formula of r=r0+vt? :confused:

    Also, to find c) I need to get the equation at b) first right?
    For part (b) you need to use r=r0+vt, and you need to sub in the velocity which you found in part (a).
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    (Original post by raheem94)
    For part (b) you need to use r=r0+vt, and you need to sub in the velocity which you found in part (a).
    Isn't part a) asking for the bearing? I don't see any velocity equation there :confused:
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    (Original post by Akiraryuu)
    Isn't part a) asking for the bearing? I don't see any velocity equation there :confused:
    Yes, part (a) is asking for the bearing. There will be alternative techniques to do part (a) but the way i did that required to find the velocity vector.

    Just find the velocity vector and do part (b).
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    (Original post by raheem94)
    Yes, part (a) is asking for the bearing. There will be alternative techniques to do part (a) but the way i did that required to find the velocity vector.

    Just find the velocity vector and do part (b).
    Oh! I solved part a) using trig. That's the problem, I have no idea how to get the velocity vector from the two position vector equations.
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    (Original post by Akiraryuu)
    Oh! I solved part a) using trig. That's the problem, I have no idea how to get the velocity vector from the two position vector equations.
    You know the formula,  \displaystyle r=r_0+vt

    We know that  \displaystyle r_0 = -2i-4j

    We know that at 0940(which is t=2/3 if we measure time in hours)  \displaystyle r=4i-6j

    So using the formula,  \displaystyle r=r_0+vt , we get,  \displaystyle 4i-6j =-2i-4j+\frac23v
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    (Original post by raheem94)
    You know the formula,  \displaystyle r=r_0+vt

    We know that  \displaystyle r_0 = -2i-4j

    We know that at 0940(which is t=2/3 if we measure time in hours)  \displaystyle r=4i-6j

    So using the formula,  \displaystyle r=r_0+vt , we get,  \displaystyle 4i-6j =-2i-4j+\frac23v
    Oh god, why didn't I see the connection sooner? Gah. Thank you so so so much.
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    (Original post by Akiraryuu)
    Oh god, why didn't I see the connection sooner? Gah. Thank you so so so much.
    No problem.

    Do you know how to do part (c)?
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    (Original post by raheem94)
    No problem.

    Do you know how to do part (c)?
    Yep, got it. My only problem was finding the vector equation. Thanks again.
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    how do we find the time ?
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    A boat B is moving with constant velocity. At noon, B is at the point with position vector
    (3i – 4j) km with respect to a fixed origin O. At 1430 on the same day, B is at the point
    with position vector (8i + 11j) km.
    (a) Find the velocity of B, giving your answer in the form pi + qj.

    how to find the time :bricks: im stuck in this
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    (Original post by sowmyaraju)
    A boat B is moving with constant velocity. At noon, B is at the point with position vector
    (3i – 4j) km with respect to a fixed origin O. At 1430 on the same day, B is at the point
    with position vector (8i + 11j) km.
    (a) Find the velocity of B, giving your answer in the form pi + qj.

    how to find the time :bricks: im stuck in this
    i think you need to use r=Ro+vt
    so (8i+11j)=(3i-4j) + 2.5v
    (8i+11j) - (3i - 4j) =2.5v
    (5i + 15j) = 2.5v
    v= 2i + 6j
    is that the right answere?
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    What does it mean when something says find the time when X is moving 'due east of something'

    equate the i components?
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    (Original post by Obscenedilemma)
    What does it mean when something says find the time when X is moving 'due east of something'

    equate the i components?
    If X moves due east of Y then the j components of both are same, so equate the j components.
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    hey......can sm1 hlp me wid dis question
    given that a=2i+5j and b=3i-j find X if a+Xb is parallel to vector i
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    (Original post by backstreet1)
    hey......can sm1 hlp me wid dis question
    You need to start a thread not add to an old one

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