a. Write your own MATLAB program to determine the time to reach a falling distance of 100 m using the composite Simpson's rule (with n - 10 segments) combined with Newton Raphson method for the root finding with a relative error less than 0.1%. Tabulate the results and errors of each iteration. Start with the initial guess of lo-12 sec for the Newton Raphson method. b. Suppose that the actual velocity of the parachutist at known values of time is measured and given in the following table: Time (2 345678910 12 13 14 15 Measured 10 16.3 23 27.5 31 35.6 39 41.5 42.9 45 46 45.5 46 49 50 velocity (m/s) write a MATLAB code using linear least-square regression to determine the coefficients and in an alternative empirical model for the velocity of the parachutist: + t Also, plot both measured and fitted results on the same figure. a. Write your own MATLAB program to determine the time to reach a falling distance of 100 m using the composite Simpson's rule (with n - 10 segments) combined with Newton Raphson method for the root finding with a relative error less than 0.1%. Tabulate the results and errors of each iteration. Start with the initial guess of lo-12 sec for the Newton Raphson method. b. Suppose that the actual velocity of the parachutist at known values of time is measured and given in the following table: Time (2 345678910 12 13 14 15 Measured 10 16.3 23 27.5 31 35.6 39 41.5 42.9 45 46 45.5 46 49 50 velocity (m/s) write a MATLAB code using linear least-square regression to determine the coefficients and in an alternative empirical model for the velocity of the parachutist: + t Also, plot both measured and fitted results on the same figure