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    Solution of Relative Velocity Problem

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    Relative Velocity Problem
    Consider a boat on the West bank of a river of width D=1664 meters to be at the origin of an x,y axis system with the 0° direction East along the +x axis.
    The river water runs South with velocity vector W= 3.9 m/sec at 270°.
    At coordinates (1200, -390) is a dock on an island. At coordinates (1664, 0) is a cabin. The boat starts at (0,0), pointing to a heading of 0°, with unknown speed B relative to the water. Combined with the current velocity, it moves in a straight line to the dock with actual velocity A, arriving in 100 seconds.
    Carefully observe the problem attachment, a picture illustrating all given
    information in Fig. 1.
    a. Find the magnitude and direction of
    actual velocity vector A.
    b. Construct a polygon connecting vectors
    W, B, and A. Solve this vector
    triangle, Fig. 2, to find B, the speed of
    the boat relative to the water.
    c. With B, the boat's speed relative to the
    water, known from part b, the
    boat now heads in a direction such that
    it travels in a straight line to the
    cabin with velocity over ground vector V.
    Find the required heading of the boat
    and the time to move from dock to

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    Solution Preview

    Solution of Relative Velocity Problem
    a. The distance from origin to dock is;
    D=sqrt(1200^2+390^2)= 1262 m
    which the boat travels in 100 seconds.
    Therefore, the speed of the boat, (the
    magnitude of vector A), is:
    A=D/t= 1262 m/100 sec = 12.62 m/sec.
    The line from origin to dock is at angle
    p° = invtan (-390/1200) = -18° and ...

    Solution Summary

    A Solution of Relative Velocity Problem is provided. The magnitude and direction is found.