Question

(hrw8c9p16) Ricardo, mass 80 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 23.9 cm relative to a submerged log during the exchange and calculates Carmelita's mass, which she has not told him. What is it?

**Carmelita's weight**

Answer 1

Let coordinates of Carmelita, center of the canoe and Ricardo are 0 m, 1.5 m and 3 m, respectively.

Their coordinates after the exchange will be 0.239 m (Ricardo), 1.739 m (center of the canoe) and 3.239 (Carmelita).

Let “x” is the mass of Carmelita.

The total mass of the system is 80+30+x = 110 + x kilograms.

The coordinate of the center of mass in meters before the exchange is
(0*x + 1.5*30 + 3*80) / (110 + x)

The coordinate of the center of mass in meters after the exchange is
(0.239*80 + 1.739*30 + 3.239*x) / (110 + x)

The center of mass did not move, therefore both the above values must be equal:
(0*x + 1.5*30 + 3*80) / (110 + x) = (0.239*80 + 1.739*30 + 3.239*x) / (110 + x)
0*x + 1.5*30 + 3*80 = 0.239*80 + 1.739*30 + 3.239*x

=> 45 + 240 = 19.12 + 52.17 + 3.239*x

=> 3.239*x = 213.71

=> x = 65.98 kg.