A spherical float with a mass of mf = 70 kg and a diameter of 90 cm is placed in the ocean (density of sea water is approximately p = 1030 kg/m3. The height, h, of the portion of the float that is above water can be determined by solving the following equation (according to Archimedes' principle):

where, for a sphere of radius r, the volume of a cap Vcap of depth d is

Write the equation in terms of h and solve for h. Use the MATLAB userdefined function, which you already created, to utilize the Newton-Raphson method. The initial guess is h1 = 80 cm and the stopping criteria should be 10 iterations. The answer should include the commands to setup the problem on MATLAB, call the user-defined function, and the tabulated results for each iteration. Plot the estimated relative error vs. the iteration number. Also, write a code that uses the MATLAB built-in function to solve for h. Use this answer as the true value and compute the true relative error.

cap m cap m