Position of Center Mass Question

AI Thread Summary
The discussion revolves around a physics problem involving the movement of a boat as two individuals shift their positions. The key equation for determining the center of mass (x_cm) is provided, which incorporates the masses of Romeo, Juliet, and the boat. The initial attempt at solving the problem involved setting equations for the center of mass before and after Juliet moves, but the user initially arrived at an incorrect distance. Ultimately, the user indicated they found the solution but expressed uncertainty about their understanding of the process. The thread highlights the importance of grasping the concept of center of mass in a closed system.
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Homework Statement



Romeo (80.0 kg) entertains Juliet (58.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.80 m away from Juliet, who is in the front of the boat. After the serenade, Juliet carefully moves to the rear of the boat (away from shore) to plant a kiss on Romeo's cheek. How far does the 85.0 kg boat move toward the shore it is facing?

___________ m

Homework Equations



x_cm = (m1*x1 + m2*x2 + ... ) / (m1 + m2 + ... )

The Attempt at a Solution



Im kind of confused on this problem and really need help..

So far I was trying to figure it out but i think i went the wrong way.. My thinking was that there was no external force on the system, so we could just set two equtions equal to each other.

In doing so i came out with..

Initially, x_cm = [(m_B * L/2) + (m_J * L)] / (m_R + m_B + m_J)

and

Now, x_cm = [ m_B*(d + L/2) + d*(m_R * m_J) ] / [m_R + m_B + m_J]

After setting those equal and solving for d, i came out with .03437m which was the wrong answer..

Can anyone please help me and lead me in the right direction?
 
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nevermind, i somehow got it, not sure i completely understand it, but i will in time =]
 

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