(Solution) - A water tank shaped as an ellipsoid a 1 5 -(2025 Original AI-Free Solution)

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A water tank shaped as an ellipsoid (a = 1.5 m, b = 4.0 m, c = 3m) has a circular hole at the bottom, as shown. According to Torricelli's law, the speed v of the water that is discharging from the hole is given by
v = ?2gh
where h is the height of the water and g = 9.81m/s2. The rate at which the height, h, of the water in the tank changes as the water flows out through the hole is given by

where rh is the radius of the hole.
Solve the differential equation for y. The initial height of the water is h = 5.9 m. Solve the problem for different times and find an estimate for the time when h = 0.1 m. Make a plot of y as a function of time.