Final answer:
A cargo barge will sit at a different depth in a freshwater river compared to a saltwater harbor due to the difference in water density. The barge must displace a greater volume of freshwater to float, which implies a deeper draft in the river. The depth the barge will sit in the river is approximately 0.91 m.
Step-by-step explanation:
The depth of the cargo barge in the river can be determined by understanding the concept of buoyancy. The barge displaces a certain volume of water equal to its weight. The weight of the barge in saltwater can be calculated by multiplying the volume of the barge submerged in the saltwater harbor by the density of saltwater, which is approximately 1025 kg/m³. Similarly, the weight of the barge in freshwater can be calculated by multiplying the volume of the barge submerged in the freshwater river by the density of freshwater, which is approximately 1000 kg/m³.
Given that the dimensions of the barge are 3.5 m by 22.0 m and it sits 0.90 m deep in the saltwater harbor, the volume of the barge submerged in saltwater is 3.5 m * 22.0 m * 0.90 m = 69.3 m³. Therefore, the weight of the barge in saltwater is 69.3 m³ * 1025 kg/m³ = 70972.5 kg.
Using the same dimensions of the barge, the volume of the barge submerged in freshwater can be calculated as 3.5 m * 22.0 m * x = 69.3 m³ (x is the depth the barge will sit in the river). Rearranging the equation, we have x = 69.3 m³ / (3.5 m * 22.0 m). Solving the equation, the depth the barge will sit in the river is approximately 0.91 m.