Final answer:
The depth at which the barge will sit in the river depends on the water's density, which is determined by Archimedes' principle and the concept of buoyancy in Physics.
Step-by-step explanation:
The question relates to the concept of buoyancy and Archimedes' principle in Physics, which states that the upward buoyant force exerted on a body immersed in a fluid is equal to the weight of the fluid that the body displaces. The depth at which the rectangular barge sits in the harbor is given, and the student is asked to calculate how deep it will sit in the river. To solve this problem, one must consider the density of the harbor water and river water, assuming the barge carries the same weight in both cases. If the density of the water in both the harbor and the river is the same, then the barge will sit at the same depth of 0.80 m in the river. If not, the densities must be taken into account to find the new depth using the formula for buoyant force.