What is the final speed of the boat?

[Westin]

Homework Statement

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 and its speed is 4.6m[PLAIN]https://s3.lite.msu.edu/adm/jsMath/fonts/cmmi10/alpha/144/char3D.pngs. 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, 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, 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.

What is the final speed of the boat?[/B]

Homework Equations

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

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![/B]

 

[TSny]

3) Final Velocity = KE/m

This is not the correct relation between velocity and KE.

 

[Westin]

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?

 

[TSny]

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?