From Torricelli’s law, water in an open tank will flow out through a hole in the bottom at...

From Torricelli’s law, water in an open tank will flow out through a hole in the bottom at a speed equal to that it would acquire in a free-fall from the level of the water to the hole. A parabolic bowl has the shape of y = x2, 0 ≤ x ≤ 1, (units are feet) revolved around the y-axis. This bowl is initially full of water and at t = 0, a hole of radius a is punched at the bottom. How long will it take for the bowl to drain? Hint: An object dropped from height h will hit the ground at a speed of , where g is the gravitational constant. This formula is derived from equating the kinetic energy on impact, (1/2)mv2, with the work required to raise the object, mgh.