How Can Ricardo Calculate Carmelita's Mass Based on Their Movement in a Canoe?

[darkys]

i have this problem that I've been trying to figure out for a while, and can't seem to get it.

Ricardo, of mass 87 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 28 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.3 m apart and symmetrically located with respect to the canoe's center. Ricardo notices that the canoe moves 57.6 cm horizontally relative to a pier post during the exchange and calculates Carmelita's mass. What is it?

ive been trying this from many different ways. I've tried using the canoe after they move as the center of gravity, and then using x as the mass of the girl. I multiply the masses time the distance away from the center of gravity(the canoe) all divided by the mass, but its not coming out to the right answer. Can anyone help me with this?

 

[Andrew Mason]

i have this problem that I've been trying to figure out for a while, and can't seem to get it.

Ricardo, of mass 87 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 28 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.3 m apart and symmetrically located with respect to the canoe's center. Ricardo notices that the canoe moves 57.6 cm horizontally relative to a pier post during the exchange and calculates Carmelita's mass. What is it?

ive been trying this from many different ways. I've tried using the canoe after they move as the center of gravity, and then using x as the mass of the girl. I multiply the masses time the distance away from the center of gravity(the canoe) all divided by the mass, but its not coming out to the right answer. Can anyone help me with this?

The centre of mass of a system is defined as the point where:

\sum_{i=0}^n m_i\vec{x_i} = 0

where xi is the displacement of the centre of mass of each mass object in the system from the centre of mass of the system.

So set up an equation where there are three displacement vectors representing the displacement of the cm of each of the two people and the canoe from the cm of the system, both before and after the switch. Since the cm does not change, these are equal. You know that the sum of the displacements of C and R is the distance between the seats. You also know the difference between the positions of the cm of the canoe. So you have 3 equations, 3 variables. You should get a unique solution.

AM