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What is the final speed of the boat?

  1. Feb 27, 2015 #1
    1. The problem statement, all variables and given/known data

    Jack and Jill are maneuvering a 3570kg boat near a dock. Initially the boat's position is [PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char68.png2,0,9[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char69.pngm [Broken] and its speed is 4.6m[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngs. [Broken] As the boat moves to position [PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char68.png12,0,0[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char69.pngm, [Broken] Jack exerts a force of [PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char68.png-80,0,290[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char69.pngN, [Broken] and Jill exerts a force [PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char68.png0,240,0[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmsy10/alpha/144/char69.pngN. [Broken]

    What is the final speed of the boat?



    2. Relevant equations

    W=Fd
    Kfinal = Kinitial +W
    KE=(1/2)mv^2



    3. The attempt at a solution

    1) Final total work

    Jack Work = (-80*10)+(0*0)+(290*-9) = -3410
    Jill Work = 0

    (It says my Work is correct)

    2) Kfinal = Kinitial + W
    Kinitial = (1/2)(3570)(4.6)^2 = 37770.6

    Kfinal = 37770.6+(-3410)
    Kfinal = 34360.6

    3) Final Velocity = KE/m
    34360.6/3570 = 9.6248m/s

    Not sure where my error is... any help would be appreciated!



     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Feb 27, 2015 #2

    TSny

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    Homework Helper
    Gold Member

    This is not the correct relation between velocity and KE.
     
  4. Feb 27, 2015 #3
    I was able to get the worst answer, I just plugged final KE back into K= 1/2mv^2 and solved for v.

    The second part of the question asks... Which person exerted a force perpendicular to the displacement of the boat?
    a) Neither Jack nor Jill.
    b) Both Jack and Jill.
    c) Jill
    d) Jack.

    I thought it was Jack since Jack is the only person exerting Work. But then I thought Jill because she's exerting force, but just in the wrong direction (perpendicular?) so her work is 0. I only have one shot at this, is my reasoning ok for saying its Jill?
     
  5. Feb 27, 2015 #4

    TSny

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    Homework Helper
    Gold Member

    Have you covered the "dot product" or "scalar product" of two vectors? If so, you probably covered how to use the dot product to test if two vectors are perpendicular.

    If you are not familiar with the dot product, then can you sketch the two force vectors and the displacement vector on a x,y, z coordinate system?
     
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