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Math Help - Vector Question

  1. #1
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    Vector Question

    We are studying Vectors at the moment and I am really confused about this one question. If someone could help me it would be greatly appreciated. Please and thank you.

    1. A boat travels in a straight line across a bay from point A to point B, a distance of 20 nautical miles on a bearing of 065o. A tide in the bay moves on a bearing of 105o at 3 knots. If the boat’s speed in still water is 10 knots,

    (i) Draw a triangle of velocities showing the information given.

    (ii) Find the direction in which the boat must be steered so that it travels along the straight line segment joining A to B.
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  2. #2
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    Triangle of Velocities

    Hello ohsoconfused
    Quote Originally Posted by ohsoconfused. View Post
    We are studying Vectors at the moment and I am really confused about this one question. If someone could help me it would be greatly appreciated. Please and thank you.

    1. A boat travels in a straight line across a bay from point A to point B, a distance of 20 nautical miles on a bearing of 065o. A tide in the bay moves on a bearing of 105o at 3 knots. If the boat’s speed in still water is 10 knots,

    (i) Draw a triangle of velocities showing the information given.

    (ii) Find the direction in which the boat must be steered so that it travels along the straight line segment joining A to B.
    In the attached diagram:

    • _BV_E is the velocity of the boat relative to the earth. This is in a direction 065^o, since that is the direction the boat needs to move.


    • _BV_W is the velocity of the boat relative to the water. This is 10 units (knots) in magnitude. Its direction gives the direction in which the boat will need to steer.


    • _WV_E is the velocity of the water relative to the earth; in other words, the tide or current at 3 knots in a direction 105^o.

    These vectors are connected by the equation _BV_W+_WV_E=_BV_E. Notice two things:

    • The order of the letters B, W, E in this equation: they go B..W + W..E = B..E, just like a displacement vector equation such as \vec{AB} +\vec{BC} = \vec{AC}


    • In the diagram, the arrows on the two vectors that are added (that's _BV_W+_WV_E) follow one another around the triangle. The resultant, or sum, of these two vectors is the third vector _BV_E.

    So that's how the diagram is drawn. You'll need to use the Sine Rule to calculate the angle between _BV_W and the North, to give you the bearing that the boat must steer. Can you complete this now?

    Grandad
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