Position of Center Mass Question

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SUMMARY

The problem involves calculating the movement of a boat when Juliet moves from the front to the rear while Romeo plays guitar. Using the center of mass formula, x_cm = (m1*x1 + m2*x2 + ...) / (m1 + m2 + ...), the initial and final positions of the center of mass must be equated to find the distance the boat moves towards the shore. The correct approach involves setting the equations for the center of mass before and after Juliet's movement equal to each other. The final answer for the boat's movement is approximately 0.03437 meters, although the user initially miscalculated.

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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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