Consider a water tank with a hole of area a in its base. The tank will drain through this hole, at a rate proportional to the height of the water (as this influences the pressure). Torricelli's Law describes this process: dh 2gh(t). dt where: h(t) = the height of water in the tank at time t in m, A = is the cross-sectional area of the tank in m?, a = the area of the hole in the bottom of the tank in m2, and g = 9.81 m/s is the acceleration due to gravity. For the following questions, use A = 10 m, a = 0.1 m?, and h(0) = 10 m. 1. Solve the ODE using separation of variables. 2. Use a first order Taylor series to show that when Torricelli's law is linearised about the initial height, we get dh a AV 2h(0) (h(t) + h(0)) dt 3. Solve the linearised ODE using the integrating factor method. 4. Plot your solutions to Q1 and Q3 in the same figure. Discuss the accuracy of the linearised ODE solution.