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

Answer:

65.14925 kg

Explanation:

Center of mass before the exchange

$X_{c1}=\dfrac{0+1.5\times 20+3\times 85}{85+20+x}$

Center of mass after exchange

$X_{c2}=\dfrac{0.35\times 85+(0.35+1.5)\times 20+(3+0.35)\times x}{85+20+x}$

The center of mass remains constant so $X_{c1}=X_{c2}$

$\dfrac{0+1.5\times 20+3\times 85}{85+20+x}=\dfrac{0.35\times 85+(0.35+1.5)\times 20+(3+0.35)\times x}{85+20+x}\\\Rightarrow 1.5\times 20+3\times 85=0.35\times 85+(0.35+1.5)\times 20+(3+0.35)\times x\\\Rightarrow x=\dfrac{1.5\times 20+3\times 85-0.35\times 85-(0.35+1.5)\times 20}{3+0.35}\\\Rightarrow x=65.14925\ kg$

Mass of Carmelita is 65.14925 kg