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Thread: 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:

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


    • $\displaystyle _BV_W$ 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.


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

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

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


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

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

    Grandad
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