romeo (75.0 kg) entertains juliet (57.0 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. what if? if the lovers both walk toward each other and meet at the center of the boat, how far (in m) and in what direction does the boat now move?

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12-10-2022
Physics

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romeo (75.0 kg) entertains juliet (57.0 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. what if? if the lovers both walk toward each other and meet at the center of the boat, how far (in m) and in what direction does the boat now move?

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kumarprabhat kumarprabhat · Answer 1 · 2022-10-14T23:24:59-04:00

If the lovers both walk toward each other and meet at the center of the boat, at 0.725m and since romeo has greatest mass of the boat moves towards him away from the shore.

Calculating the system's center of mass should come first

X_{CM}=\sum_{n=1}^{n}\frac{X_n*M_n}{M_n}

Romeo, Juliet, and the boat's masses are multiplied by each coordinate's x value, and the result is then divided by the sum of all the masses.referring to Juliet's position as an example.

X_{CM}=\frac{57Kg\times0m+75Kg\times 2.7m+75kg\times1.35m}{57kg+75kg+75kg}

X_{CM}=\frac{307.395kg.m}{207kg}=1.485m

When internal forces are in play, the center of mass remains constant.

After the maneuver, the center of mass shifts in relation to the back of the boat, but it stays at the same distance from the shore.

X_{CM}=\frac{75\times1.35m+(75kg+57kg)\times2.70m}{207kg}=

X_{CM}=\frac{457.65}{207kg}=2.210m

The boat moves toward the shore with this displacement.

0.725m

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