1. **Problem statement:** Calculate the buoyant force acting on a rectangular vertical surface submerged in water. The surface dimensions are 3 m by 7 m, and the top of the surface is 2.5 m below the water surface. 2. **Relevant formula:** The buoyant force $F_b$ on a submerged surface is given by the hydrostatic force formula: $$F_b = \rho g A \bar{h}$$ where: - $\rho$ is the density of water (approximately 1000 kg/m³), - $g$ is the acceleration due to gravity (approximately 9.8 m/s²), - $A$ is the area of the submerged surface, - $\bar{h}$ is the depth of the centroid of the surface below the water surface. 3. **Calculate the area $A$:** $$A = 3 \times 7 = 21 \text{ m}^2$$ 4. **Calculate the depth of the centroid $\bar{h}$:** Since the surface is vertical and rectangular, the centroid is at the midpoint of its height. The top is 2.5 m below the surface, and the height is 3 m, so: $$\bar{h} = 2.5 + \frac{3}{2} = 2.5 + 1.5 = 4.0 \text{ m}$$ 5. **Calculate the buoyant force $F_b$:** $$F_b = 1000 \times 9.8 \times 21 \times 4.0 = 823200 \text{ N}$$ 6. **Interpretation:** The buoyant force acting on the surface is 823200 newtons, directed upward due to the pressure of the water. **Final answer:** $$F_b = 823200 \text{ N}$$