Who is sitting in the rear of their boat in still water, entertains Juliet by playing his guitar. After the song, Juliet, who was sitting in the front of the boat (closest to shore), carefully moves to the rear to plant a kiss on Romeo's cheek. The 100-kg boat is facing shore and the 50 kg Juliet moves towards the 70 kg Romeo. The length of the boat is 4 m, and we can neglect water resistance when the boat moves. How far does the boat move? Does it move toward or away from the shore?

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Question:

who is sitting in the rear of their boat in still water, entertains Juliet by playing his guitar. After the song, Juliet, who was sitting in the front of the boat (closest to shore), carefully moves to the rear to plant a kiss on Romeo's cheek. The 100-kg boat is facing shore and the 50 kg Juliet moves towards the 70 kg Romeo. The length of the boat is 4 m, and we can neglect water resistance when the boat moves. How far does the boat move? Does it move toward or away from the shore?

Answers

Answer:Δx = -1.27 m the boat moves away from the shoreExplanation:Let's analyze the exercise a little, to know when the boat has moved, we can fixate on a point, let's use the point of the center of mass, before and after the movement of people. The center of mass is defined by.            [tex]x_{cm}[/tex]= 1 /M ∑ m_i  x_i where M is the total mass of the object, x_i and m_i are the positions and masses of each part of the system.        let's find the total mass            M = m_boat + m_Juliet + m_Romeo          M = 100 + 50 + 70          M = 220 kg now let's look for the center-mass position initial. Before the movement of people        x_{cm1} = 1/M (x_boat m_boat + x_juliet  m_juliet + x_romeo m_romeo) Let's find the position of each object, let's fix our reference system on the front of the boat The boat its center of mass coincides with its geometric center        x_boat = 2 m Julliet is sitting in the front of the boat        x_juliet = 0 m Romeo is sitting in the back of the boat        x_romeo = 4 m we substitute       x_{cm1} = 1/220 (2 100 + 50 0 + 70 4)       x_{cm1} = 2.1818 m final. After the movement of people positions boat      x_boat = 2 m Juliet      x_juliet = 0 m Romeo      x_romeo = 0 m we substitute      x_{cm2} = 1/220 (2 100 + 50 0 + 500 0)      x_{cm2} = 0.9090 m the movement of the boat is     Δx = x_cm2 - xcm1     Δx = 0.9090 - 2.1818     Δx = -1.27 m The negative sign indicates that the boat moves in the opposite direction to the movement of people, therefore the boat moves away from the shore

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