Changing places in canoe - find mass

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In the discussion, the problem involves Ricardo and Carmelita exchanging seats in a canoe while maintaining the center of mass of the system. Ricardo's mass is 82 kg, and the canoe weighs 38 kg. During the seat exchange, the canoe moves 58.4 cm, indicating a shift in the center of mass. To find Carmelita's mass, denoted as m, the initial and final positions of the center of mass must be set equal, considering the canoe's movement. By applying the principle of conservation of momentum and the center of mass formula, the calculation reveals Carmelita's mass.
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Ricardo, of mass 82 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 38 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.1 m apart and symmetrically located with respect to the canoe's center. Ricardo notices that the canoe moves 58.4 cm horizontally relative to a pier post during the exchange and calculates Carmelita's mass. What is it?

Thankz to anyone who can show how to solve this really appreciate it.
 
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Think center of mass. There is no net force acting on the system of Ricardo+Carlita+boat... so the center of mass must remain motionless.

Call carlita's mass m.

Take a fixed axis from which you measure the position of the center of mass...

what is the initial position of the center of mass from this axis in terms of m?

what is the final position of the center of mass from this axis in terms of m (remember that the boat moves 58.4cm)?

initial position = final position...
 
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