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?

Answer 1

Δx = -1.27 m

the boat moves away from the shore

Step-by-step explanation:

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.

`x_(cm)`= 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