Changing places in canoe - find mass

[Dynex]

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.

 

[learningphysics]

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...

 

[ogb p]

To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant unless acted upon by an external force. In this case, the system consists of Ricardo, Carmelita, and the canoe.

First, we need to calculate the initial momentum of the system before the seat exchange. This can be done by multiplying the mass of each person by their initial velocity (which is zero since they are at rest). The total initial momentum of the system is therefore zero.

After the seat exchange, the canoe moves 58.4 cm horizontally relative to the pier post. We can use this information to calculate the final momentum of the system. Since the canoe is the only object moving horizontally, its momentum is equal to its mass (38 kg) multiplied by its final velocity, which we can calculate using the distance (58.4 cm) and the time it took for the seat exchange (which is not given in the problem).

To find Carmelita's mass, we can set up an equation using the principle of conservation of momentum: initial momentum = final momentum. This would be 82 kg (Ricardo's mass) multiplied by 0 (since he is now at rest) = 38 kg (canoe's mass) multiplied by the final velocity of the canoe.

Solving for the final velocity, we get a value of 0.1526 m/s.

Now, we can use this final velocity to calculate Carmelita's mass. We know that her mass plus Ricardo's mass (82 kg) must equal the mass of the canoe (38 kg) plus her mass multiplied by the final velocity of the canoe.

Setting up this equation, we get: 82 kg + Carmelita's mass = 38 kg + Carmelita's mass x 0.1526 m/s.

Solving for Carmelita's mass, we get a value of approximately 27.3 kg. Therefore, Carmelita's mass is approximately 27.3 kg.