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Thread: girl crossing a river

  1. #1
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    girl crossing a river

    a ship k is travelling at 25 km/h . another ship is h is travelling east at 17 km/h. to an observer on ship h, ship k appears to be travelling north east..<br>find the velocity of ship k<br><br>what I have tried.<br>  &nbsp;Vk = 25cosa i +25sina j <br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Vh=17i &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Vkh= (25cosa-17)i +25sinaj &nbsp;&nbsp;<br><br>i and j &nbsp;is equal as its in a north east direction&nbsp;<br>25cosa-17=25sina<br>I have a feeling I am going no where<br><br><br><br>
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    Re: girl crossing a river

    never mind top post
    a ship k is travelling at 25 km/h . another ship is h is travelling east at 17 km/h. to an observer on ship h, ship k appears to be travelling north east..find the velocity of ship k

    what I have tried. Vk = 25cosa i +25sina j Vh=17i Vkh= (25cosa-17)i +25sinaj
    i and j is equal as its in a north east direction
    25cosa-17=25sina
    I have a feeling I am going no where
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  3. #3
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    Re: girl crossing a river

    Okay, Vk = 25cosa i +25sina j where a is the angle the ships direction makes with the i, therefore, east, direction.
    The second ship, h, is moving east at 17 km/h so its velocity vector is 17i The velocity of h relative to k is (17-25cos(a))i- 25sin(a)j. Since that is "north-east" we must have 17- 25cos(a)= -25 sin(a).

    Squaring both sides of the equation, 289- 50cos(a)+ 625 cos^2(a)= 625 sin^2(a) Let cos(a)= y. Then sin^2(a)= 1- cos^2(a) so the equation becomes 290- 50 y+ 625y^2= 625- 625y^2 or 1300y^2- 50y- 335= 0.
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    Re: girl crossing a river

    I get cos a=.5272289. ( The other answer is negative)
    It is not working out for me .
    The right answer at the back of the book is 24i+7j
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  5. #5
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    Re: girl crossing a river

    ship h vector + relative vector = ship k vector

    $17i + (ai + aj) = (17+a)i + aj$

    $(17+a)^2 + a^2 = 25^2$

    $a^2+17a-168=0$

    $(a+24)(a-7)=0$

    $a > 0 \implies a=7$

    ship k vector = $24i+7j$
    Thanks from markosheehan
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    Re: girl crossing a river

    when writing down the vector of ship k should it not be split up into i and j components. when using Vkh=Vk-Vh i was told to always split the vectors into i and j components, but you leave it as 25
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  7. #7
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    Re: girl crossing a river

    first equation's right side is ship k's velocity vector written in component form ...

    second line is the magnitude of ship k's velocity vector

    $\sqrt{(17+a)^2 + a^2} = |v_k| = 25$

    square both sides and solve for $a$
    Last edited by skeeter; Jun 19th 2017 at 04:11 AM.
    Thanks from markosheehan
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