Ricardo, mass 88 kg and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 30 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.0 m apart and symmetrically located with respect to the center of the canoe. Ricardo notices that the canoe moved 63.5 cm relative to a submerged log during the exchange and calculates Carmelita's mass, which she has not told him. What is it?

Question

Ricardo, mass 88 kg and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 30 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.0 m apart and symmetrically located with respect to the center of the canoe. Ricardo notices that the canoe moved 63.5 cm relative to a submerged log during the exchange and calculates Carmelita's mass, which she has not told him. What is it?

Answer 1

mr..........|..............mc

mc..............|..........mr

The vertical bar | represents the centre of gravity of the masses of the two persons, mr for Ricardo, and mc for Carmelita.
When they exchange seats, they exert a force on the canoe in such a way that the heavier person pushes more on the canoe. The centre-of gravity (in theory) remains at the same place.

Therefore (3 - 0.635)/2=1.1825 is the location of centre of gravity from Ricardo.
We have therefore:
mr*1.1825=mc*(3-1.8175)
mc=mr*1.1825/1.8175
=57.25 kg

Check my thinking.

Answer 2

To determine Carmelita's mass, we can apply the principle of conservation of momentum. This principle states that the total momentum of an isolated system remains constant if no external forces act on it.

In this scenario, the system consists of Ricardo, Carmelita, and the canoe. Initially, the canoe is at rest, and after the seat exchange, the canoe moves relative to the submerged log. The momentum of the system before and after the seat exchange must be equal.

The formula for momentum is:

P = m * v

where P represents momentum, m represents mass, and v represents velocity.

Let's break down the given information:

Mass of Ricardo (mRicardo) = 88 kg
Mass of the canoe (mCanoe) = 30 kg
Distance between the seats (d) = 3.0 m
Displacement of the canoe (Δx) = 63.5 cm = 0.635 m (since momentum depends on displacement, not distance).

Initially, Ricardo and Carmelita are at rest, so their velocities are zero. Since the canoe is at rest as well, its velocity is also zero.

Before the seat exchange:
Total momentum (P_initial) = (mRicardo + mCanoe) * 0

After the seat exchange:
Momentu