1. The water jug A cubic box (of side L=3 m) is initially filled with water up to a height h. The water flows out of the box through a circular hole cut in the bottom. The diameter of the hole is d = 0.1 m. (a) Derive a differential equation for h = h(t) where t is time. Hint: you will need to use the Torricelli's law which expresses the velocity of the water flowing through the hole for a given height h: v = v2gh. Here g is the acceleration due to gravity. (b) solve the differential equation using h(0) = 2 m as initial condition. (c) find how much time elapses until the box is completely empty, for h(0) = 2 m. (d) graph (hand-drawing acceptable) the function h(t)