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Romeo (85.0 kg) entertains Juliet (59.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.70 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. (a) How far (in m) does the 75.0 kg boat move toward the shore it is facing? m

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boffeemadrid

Answer:

0.7274 m

Explanation:

X denotes the distance from the reference point

M denotes the mass of the point

The center of mass of a system is given by

[tex]X_{CM}=\sum_{n=1}^n\frac{X_n\times M_n}{M_n}[/tex]

Taking the position of Juliet as the reference point

[tex]X_{CM}=\frac{59\times 0+85\times 2.7+75\times 1.35}{59+85+75}\\\Rightarrow X_{CM}=1.51027\ m[/tex]

After the boat has moved the distance between the center of mass of the boat and the shore remains the same. The change is observed relative to the rear of the boat

[tex]X_{CM}=\frac{75\times 1.35+(85+59)\times 2.7}{59+85+75}\\\Rightarrow X_{CM}=2.23767\ m[/tex]

The displacement of the boat towards the shore is

[tex]2.23767-1.51027=0.7274\ m[/tex]

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