Respuesta :
Answer:
0.69m
Explanation:
Assume the boat is uniform and so its centroid is at its center, which is midpoint between Romeo and Juliet
Let's pick a stationary reference line at Romeo's end of the boat. We can calculate the centroid position with respect to this point of the system consisting of Romeo R, boat b and Juliet J:
[tex]m_Rx_R + m_bx_b + m_Jx_J = (m_R + m_b + m_J)x[/tex]
[tex]79*0 + 75*(2.7/2) + 53*2.7 = (79 + 75 + 53)x[/tex]
[tex]244.35 = 207x[/tex]
[tex]x = 1.18m[/tex]
After Juliet moved, she would be standing at Romeo position. The centroid now would change, with respect to Romeo:
[tex]m_Rx_R + m_bx_b + m_Jx_{J2} = (m_R + m_b + m_J)x_2[/tex]
[tex]79*0 + 75*(2.7/2) + 53*0 = (79 + 75 + 53)x_2[/tex]
[tex]101.25 = 207x_2[/tex]
[tex]x_2 = 0.49 m[/tex]
But, since there's no external force outside the system. There's shouldn't by any change in the system's centroid position. So if it stays in the same place, that means the boat much have shifted toward the shore by a distance of 1.18 - 0.49 = 0.69m
The distance the 75kg boat move toward the shore is 0.648m
Data;
- Mass of Romeo = 79kg
- Mass of Juliet = 53kg
- The distance between the boat and Juliet = 2.70m
Center of mass of the System
To solve this problem, we have to calculate the center of mass of the system.
[tex]X_c_m = \frac{(53*0)+(79*2.7)+(75*1.35)}{79+53+75} \\X_c_m = 1.52m[/tex]
The center of mass does not change when the forces are involved are internal. After the movement the center of mass remains in the same direction from the shore, but change relative to the rear of the boat.
[tex]X_c_m = \frac{(75*1.35)+(79+53)*2.7}{57+79+75} \\X_c_m = 2.168m[/tex]
The distance between is
[tex]2.168 - 1.52 = 0.648m[/tex]
The distance the 75kg boat move toward the shore is 0.648m
Learn more on center of mass here;
https://brainly.com/question/874205
