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Math Help - problem with vector velocity

  1. #1
    Newbie mayta's Avatar
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    problem with vector velocity

    i'm not a fan a vector velocities and relative velocity..so this is my predicament

    In this question, i is a unit vector due east and j is a unit vector due north.
    At 0900 hours a ship sails from the point P with position vector (2i + 3j) km relative to an origin 0. The ship sails north-east with a speed of 15 km/h

    (i) Find, in terms of i and j, the velocity of the ship.

    (ii) Show that the ship will be at the point with position vector (24.5i + 25.5j) km at 1030 hours.

    (iii) Find, in terms of i, j and t, the position of the ship t hours after leaving P.

    At the same time as the ship leaves P, a submarine leaves the point Q with position vector (47i 27j) km. The submarine proceeds with a speed of 25 km/h due north to meet the ship.

    (iv) Find, in terms of i and j, the velocity of the ship relative to the submarine.

    (v) Find the position vector of the point where the submarine meets the ship.

    any help would be appreciated
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  2. #2
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    In this question, i is a unit vector due east and j is a unit vector due north.
    At 0900 hours a ship sails from the point P with position vector (2i + 3j) km relative to an origin 0. The ship sails north-east with a speed of 15 km/h

    problem statement is poorly written ... for part (ii) to work out, the statement "The ship sails north-east with a speed of 15 km/h" should say that the ship sails 15 km/hr east and 15 km/hr north. As written, it gives one the impression that the ship's velocity is 15 km/hr in the NE direction.

    (i) Find, in terms of i and j, the velocity of the ship.

    v = 15i + 15j

    (ii) Show that the ship will be at the point with position vector (24.5i + 25.5j) km at 1030 hours.

    r(1.5) = (2i + 3j) + (15i + 15j)(1.5)

    (iii) Find, in terms of i, j and t, the position of the ship t hours after leaving P.

    r(t) = (2i + 3j) + (15i + 15j)t

    At the same time as the ship leaves P, a submarine leaves the point Q with position vector (47i 27j) km. The submarine proceeds with a speed of 25 km/h due north to meet the ship.

    (iv) Find, in terms of i and j, the velocity of the ship relative to the submarine.

    (sub velocity) + (relative velocity) = ship velocity

    relative velocity = (ship velocity) - (sub velocity)

    relative velocity = (15i + 15j) - (25j) = (15i - 10j) km/hr


    (v) Find the position vector of the point where the submarine meets the ship.

    (47i - 27j) + (25j)t = (2i + 3j) + (15i + 15j)t

    solve for t ... then determine their common position.
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  3. #3
    Newbie mayta's Avatar
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    thanks man
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