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Math Help - Mechanics: Vectors Help Needed

  1. #1
    Newbie Kiwi's Avatar
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    Mar 2008
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    Mechanics: Vectors Help Needed

    Question:
    Two Ships:

    Ship P: t=0; r= (20i + 30j) km, t=3; r= (29i + 34j) km
    Ship Q: t=0; r= (14i - 6j) km and v=12j kmh^-1

    at time t hours after midnight, position vectors of P and Q are p and q km respectively

    a) Find velocity of P in terms of i and j
    b) Find expression for p and q in terms of t, i and j
    c) at time t hours after midnight, distance between P and Q is d km
    Find expression for PQ to show that

              d^2=25t^2-92t +292

    My answers are as follows:

    a) Velocity of P is 3i +8j kmh^-1
    b) p = (20 + 3t)i + (10+ 8t)j
    q = 14i + (12t-6)j
    c) PQ = (3t - 6)i + (4t -16)j
    Therefore d^2=(3t-6)^2 + (4t-16)^2

    However, This = 25t^2 - 164t + 292

    Can anyone see where i have gone wrong, or if the question was wrong to start with?
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  2. #2
    Senior Member
    Joined
    Dec 2007
    From
    Anchorage, AK
    Posts
    276

    Error

    Your error is in the velocity of P; this propagated into the rest. The position vector of P is (20\mathbf{\hat{i}} + 30\mathbf{\hat{j}}) at t=0, and is (29\mathbf{\hat{i}} + 34\mathbf{\hat{j}}) at t=3. You had correctly that the x component of the velocity is v_x=\frac{\Delta{x}}{\Delta{t}}=\frac{29-20}{3-0}=3, but your y component is wrong: v_y=\frac{\Delta{y}}{\Delta{t}}=\frac{34-30}{3-0}=\frac{4}{3}

    So the velocity of P is (3\mathbf{\hat{i}} + \frac{4}{3}\mathbf{\hat{j}}) km/h,
    and the rest follows from there.

    I hope this helped.

    --Kevin C.
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