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Math Help - Vector problem

  1. #1
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    Vector problem

    2. A boat is heading due east at 25 km/hr (relative to the
    water). The current is moving toward the southwest at 10
    km/hr.
    (a) Give the vector representing the actual movement of
    the boat.
    (b) How fast is the boat going, relative to the ground?
    (c) By what angle does the current push the boat off of
    its due east course?


    A - I don't I'm doing it right. I have 25i +10j + 26.9k
    I used the Pythagorean theorem with a = 25 b = 10, and I solved for c.

    b - I don't know how to deal with the southwest. It would be easy if the current was going in the opposite direction of the boat.

    c- same. I don't know how to deal with the southwest direction.

    Thanks!
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  2. #2
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    Quote Originally Posted by Truthbetold View Post
    2. A boat is heading due east at 25 km/hr (relative to the
    water). The current is moving toward the southwest at 10
    km/hr.
    (a) Give the vector representing the actual movement of
    the boat.
    (b) How fast is the boat going, relative to the ground?
    (c) By what angle does the current push the boat off of
    its due east course?


    A - I don't I'm doing it right. I have 25i +10j + 26.9k
    I used the Pythagorean theorem with a = 25 b = 10, and I solved for c.

    b - I don't know how to deal with the southwest. It would be easy if the current was going in the opposite direction of the boat.

    c- same. I don't know how to deal with the southwest direction.

    Thanks!
    (a) v = [25 - 10\cos(45^\circ)]\vec{i} - 10\sin(45^\circ)\vec{j}

    v_x = 25 - 10\cos(45^\circ) ... v_y = -10\sin(45^\circ)

    (b) |v| = \sqrt{v_x^2 + v_y^2}

    (c) \theta = \arctan\left(\frac{v_y}{v_x}\right)
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