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Math Help - Vectors

  1. #1
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    Vectors

    1. Find the magnitude and direction of the resultant velocity vector for the following perpendicular velocities.

    a. a fish swimming at 3.0 m/s relative to the water across a river that moves at 5.0 m/s

    b. a surfer traveling at 1.0 m/s relative to the water across a wave that is traveling at 6.0 m/s



    2. Find the resultant displacement of a fox that heads 55 degrees north of west for 10.0 meters, then turns and heads west for 5.0 meters.
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  2. #2
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    Quote Originally Posted by rod789 View Post
    1. Find the magnitude and direction of the resultant velocity vector for the following perpendicular velocities.

    a. a fish swimming at 3.0 m/s relative to the water across a river that moves at 5.0 m/s

    b. a surfer traveling at 1.0 m/s relative to the water across a wave that is traveling at 6.0 m/s



    2. Find the resultant displacement of a fox that heads 55 degrees north of west for 10.0 meters, then turns and heads west for 5.0 meters.
    to #a):

    Use a coordinate system: Let the direction of the current be the positive x-axis, then the direction in which the fish is swimming forms the positive y-axis:

    \vec c = (5,0) .... and .... \vec f = (0,3)

    Then the resulting velocity is

    \vec r = \vec c + \vec f....I've got \vec r = (5,3)

    Calculate the length of the vector. If \vec v = (a,b) then |\vec v| = \sqrt{a^2+b^2}....I've got |\vec r| = \sqrt{34}

    to #b): This question has to be done in exactly the same way.

    to #2:

    Do you mean W55N or do you mean N55W? I'll take the first version. If this is wrong then you know at least how to do the problem.

    Use a coordinate system according the geographical directions. The positive x-axis is pointing East, the positive y-axis is pointing North.

    Then the first part of the way of the fox is:

    \overrightarrow{w_1} = 10(-\cos(55^\circ)\ ,\ \sin(55^\circ)) ........... and the second part is:

    \overrightarrow{w_2} = 5(-1, 0)

    \vec r = \overrightarrow{w_1}  + \overrightarrow{w_2} = \left( -10\cos(55^\circ)-5\ ,\ 10\sin(55^\circ) \right)

    The displacement is d = |\vec r| = 5\cdot \sqrt{(-10\cos(55^\circ)-5)^2+(10\sin(55^\circ))^2} ..........I've got |\vec r| \approx 13.5
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