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Answer:
0.64 m
Explanation:
The first thing is calculate the center of mass of the system.
now multiplying every coordinate x by the mass of each object (romeo, juliet and the boat) and dividing all by the total mass taking by reference the position of juliet.
X_cm = 1.4589 m
When the forces involved are internals, the center of mass don't change
After the movement the center of mass remains in the same distance from the shore, but change relative to the rear of the boat.
X_cm= 2.10 m
this displacement is how the boat move toward the shore.
2.10-1.46= 0.64 m
Apply the law of conservation of momentum for this situation. The law states that the momentum of a system is constant (in absence of external forces acting on it).
The 'system' in this case are the two skaters. There is no external force on the skaters. Suppose the skaters are initially standing still. The momentum in the system is 0. This value will need to remain constant, even after the mutual push (which is a set of forces from <em>inside</em> the system). So we know that
(total momentum before) = (total momentum after)
Indexing the masses and velocities by the first letter of the skaters' names:
From the last row, you can see that the skaters will have momentum of same magnitude but opposite direction, after the push off. That answers the first question: neither will have a greater momentum (both will have one of same magnitude).
Since Ricardo is heavier, from the above equality it follows that
In words, Paula has the greater speed, after the push-off.