Romeo (85.0 kg) entertains Juliet (51.0 kg) by playing his guitar from the rear

Question

Romeo (85.0 kg) entertains Juliet (51.0 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. How far does the 79.0-kg boat move toward the shore it is facing? M Water falls without splashing at a rate of 0.280 L/s from a height of 3.20 m into a 0.780-kg bucket on a scale. If the bucket is originally empty, what does the scale read 2.90 s after water starts to accumulate in it? N

Explanation / Answer

For question 1:

Here the Position of the C.G of the system remains Constant

Taking Romeo as Origin

Before move:

Xc.m * Mtotal = (M*X + mj*xj) -----> Here mj = 51 Kg and M = 79+85 = 164 Kg

After the boat moves:

Xc.m*Mtotal =(M*(x + X) + x*mj)

As there are Equal therefore

M*X + mj*xj = M*(x + X) + x*mj

mj*xj = M*x + x*mj

2.7 * 51 = 164x + 51x

Therefore

x = 137.7 / 215

x = 0.640 m

As for the second question, Post that in another question thread because I have a doubt in the solving of this problem, so, instead of post something wrong or unsure, it's better to post on another question thread.

Hope this helps

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