Case Studv: Parachute Problem The mathematical model of the parachute problem (i.e., a free-falling body near the earth's surface) is provided by the Newton's second law, F= ma, with a skydiver of mass m and an acceleration a. F is the sum of gravitational force F and a drag force Fa due to air resistance. The force due to gravity can be expressed as Fmg with g 9.81 m/s2. Air resistance is assumed to be linearly proportional to velocity and acts in an upward direction, as in Fa =-cv where c is a proportionality constant called the drag coefficient. As such, the net force is the difference between the downward and upward force. If the parachutist is initially at rest (v = 0 at 1-0), during free-fall the velocity satisfies the initial value problem: dt dt Using calculus, the velocity of the parachutist is given as the following function of time gm r(t) = l-e m where v = velocity ( m/s), g = gravity 9.81 m/s, m = mass of the parachutist and c = drag coefficient is 12.5 kg/s. Suppose we would like to know how far the parachutist with m = 08.1 kg has fallen after a certain time t, this distance is determined by: 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 to 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: 9 10 1112 13 14 15 Measured 10 16.3 23 |27. 3135.6 39 41 42.9 45 46 45.54649 50 velocit 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: v(t)- Also, plot both measured and fitted results on the same figure