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Math Help - vector angles

  1. #1
    Junior Member
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    vector angles

    A child walks due east on the deck of a ship at 4 miles per hour.
    The ship is moving north at a speed of 16 miles per hour.
    Find the speed and direction of the child relative to the surface of the water.
    Speed = mph
    The angle of the direction from the north

    I don't know what angle to find but i found the speed to be 16.4924
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Allie View Post
    A child walks due east on the deck of a ship at 4 miles per hour.
    The ship is moving north at a speed of 16 miles per hour.
    Find the speed and direction of the child relative to the surface of the water.
    Speed = mph
    The angle of the direction from the north

    I don't know what angle to find but i found the speed to be 16.4924
    The speed looks right.

    I assume you came up with the vector equation \bold v=4\bold i+16\bold j

    Thus, \parallel \bold v\parallel=\sqrt{16^2+4^2}\approx\color{red}\boxed  {16.49}

    Now, to find the angle, use \vartheta=\tan^{-1}\left(\frac{v_y}{v_x}\right), where v_y~and~v_x are the y and x components of vector \bold v.

    Does this make sense?

    --Chris
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  3. #3
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    yes it does thank you i had the equation upside down
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