A swimming pool 24 feet long and 15 feet wide has a bottom that is an inclined plane, the shallow end having a depth of 3 feet, and the deep end 10 feet. The pool is filled with water. For simplicity, take the density of water to be 60 lb/ft³. Find the hydrostatic force in pounds on the bottom of the pool. A)145,750 B)146,250 C)147,000 D)147,250 E)146,500 F)147,500 G)146,750 H)146,000

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Quizplus · Accepted Answer

The hydrostatic force on the bottom of the pool can be calculated by multiplying the area of the bottom by the average depth and then by the density of water. The area of the bottom is $24 \times 15 = 360 \, \text{ft}^2$. The average depth is $\frac{3 + 10}{2} = 6.5 \, \text{ft}$. Therefore, the hydrostatic force is $360 \times 6.5 \times 60 = 140,400 \, \text{lb}$. However, since this result does not match any of the options and considering the nature of the question, it seems there was a miscalculation in the explanation provided. The correct approach to calculate the hydrostatic force on the bottom of the pool involves considering the volume of water and the density, but the calculation provided was incorrect. The correct calculation involves the volume of water in the pool, which is not directly given by the average depth method mentioned. Given the error in the explanation, let's correct the approach:The volume of water in the pool can be considered as the volume of a trapezoidal prism, but since the question asks for the force on the bottom, we focus on the pressure due to the water directly above the bottom surface, which is uniform across the entire bottom. The force is the weight of the water, which is the product of the volume and the density of water.Given the mistake in the initial explanation, the correct step involves calculating the weight of the water:$$ \text{Volume of water} = \text{Area of bottom} \times \text{Average depth} $$However, the average depth approach was incorrectly applied to the force calculation instead of focusing on the weight of the water. The correct calculation should directly use the density of water and the gravitational force to find the hydrostatic force without needing the average depth, as the force on the bottom is due to the total weight of the water:$$ \text{Hydrostatic force} = \text{Volume of water} \times \text{Density of water} $$Given the error in the provided explanation and the lack of correct calculation steps for the options provided, the correct answer should be recalculated based on the correct formula for hydrostatic force:$$ \text{Hydrostatic force} = \text{Volume} \times \text{Density} $$Since the volume and specific calculation steps were not correctly provided in the explanation, and the initial response was incorrect, the correct answer should be recalculated with accurate information. Without the correct volume calculation, the specific option cannot be accurately determined from the provided explanation.

A Swimming Pool 24 Feet Long and 15 Feet Wide