Question

Ricardo, mass 85 kg, and Carmelita, who is lighter, are enjoying Lake Merced at dusk in a 20 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 canoe's center. Ricardo notices that the canoe moved 35 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

65.14925 kg

Step-by-step explanation:

Center of mass before the exchange

`X_(c1)=(0+1.5* 20+3* 85)/(85+20+x)`

Center of mass after exchange

`X_(c2)=(0.35* 85+(0.35+1.5)* 20+(3+0.35)* x)/(85+20+x)`

The center of mass remains constant so
`X_(c1)=X_(c2)`

`(0+1.5* 20+3* 85)/(85+20+x)=(0.35* 85+(0.35+1.5)* 20+(3+0.35)* x)/(85+20+x)\\\Rightarrow 1.5* 20+3* 85=0.35* 85+(0.35+1.5)* 20+(3+0.35)* x\\\Rightarrow x=(1.5* 20+3* 85-0.35* 85-(0.35+1.5)* 20)/(3+0.35)\\\Rightarrow x=65.14925\ kg`

Mass of Carmelita is 65.14925 kg