A swimming pool is 20 ft wide and 40 ft long and its bottom is an inclined plane, the shallow end having a depth of 4 ft and the deep end, 8 ft. Assume the pool is full of water. (Round your answers to the nearest whole number. Recall that the weight density of water is 62.5 lb/ft3.)

Estimate the hydrostatic force on one of the sides.

Question

A swimming pool is 20 ft wide and 40 ft long and its bottom is an inclined plane, the shallow end having a depth of 4 ft and the deep end, 8 ft. Assume the pool is full of water. (Round your answers to the nearest whole number. Recall that the weight density of water is 62.5 lb/ft3.) 

Estimate the hydrostatic force on one of the sides.

zenmo · Answer

$$\frac{ a }{ 40 }=\frac{ 8-x }{ 8 }, a = 40 * \frac{ 8-x }{ 8 }$$$$F = \int\limits_{0}^{4}\delta x40dx + \int\limits_{4}^{8 }\delta x 40 * \frac{ 8-x }{ 8 }dx$$$$40 \delta [ \frac{ 1 }{ 2 }x^2]_{0}^{4}+ 5 \delta [ 4x^2 - \frac{ 1 }{ 3 }x^3]_{4}^{8}$$$$(20)(\delta)(16) + (5)(\delta)[(256-\frac{ 512 }{ 3 })-(64-\frac{ 64 }{ 3 })]$$$$320 \delta + \frac{ 640 \delta }{ 3 }$$

My attempt at a solution, but the answer is wrong ....

legomyego180 · Answer

This video is pretty helpful. https://www.youtube.com/watch?v=cXNmCaTod58