Problem 3 According to Archimedes' principle, the buoyancy force (i.e. vertical upward reaction of water to an object) is equal to the weight of fluid displaced by the submerged portion of the object. Eventually, equilibrium (when possible) will occur when the buoyancy reaction is equal to the weight of the object. * For the sphere of this figure, derive the equation of vertical static equilibrium in terms of the following parameters: the height, h, of the portion of the sphere that is above the water, the radius r, the mass density of the sphere ps, and the mass density of water pw. * Then, write a MATLAB script where you use the bisection method to find the value of h for ,-200 kg/m3, andPn-1000 kg/m3. Use you which equilibrium is achieved. Use r- 1 m, ps initial bracket for h to be [0, 2r]. Run your script and print the function values and absolute bracket size (which represents error in h) for all iterations (one iteration below the other) Clearly state the error norms that you used for convergence. * Plot the function you solved above within the range [0, 2r]. Check if the solution you computed Note that the volume of a sphere is given as: V-7r, while the volume of the above-water portion of the sphere is given as: V, =-(3r-h) is the same with the one you graphically see 4 th