<s>[INST] A large container is filled with water and sealed at the top. A small hole is made in one side at the bottom of the container, allowing the water to drain out. Not long after the hole is made, the water starts to exit the hole and flows smoothly out onto the floor. Torricelli's law is often used to model the height \(h\) of the water in the container over time \(t\):
\[\frac{dh}{dt} = -\frac{a}{A(h)}\sqrt{2gh}\]
where \(a\) is the cross-sectional area of the hole, \(A(h)\) is the cross-sectional area of the water surface, \(g\) is the acceleration due to gravity and is given by \(g=9.8\) m/s\({}^{2}\), and \(h\) is the height of the water above the hole.
The container is in the shape of a cylinder with a radius of 25 cm and a hole with a radius of 1 cm. Find the height of the water at \(t=50\) s if it initially filled the container to a height of 1 m.[/INST]