A parachutist of mass 68.1 kg jumps out of a stationary hot air balloon. The air resistance force on the parachutist is assuming to be proportional to the square of the velocity with the air drag coefficient of 0.25 kg/m (See Eq.1). Fair resistance - Cv e is the drag coefficient, v is the velocity of the free falling parachutist Fair resistance is the air resistance force Eq.1 Apply analytical method to verify the following equation (Eq.2) for calculating the velocity of the free falling parachutist v(t)- gm tanh 96 dx 1 1+x Hint: 221- v is the velocity of the free falling parachutist m is the mass of the parachutist, 68.1 kg g is the gravitational constant, 9.81 m/s c is the air draft coefficient, 0.25 kg/m t is time in seconds tanh is the hyperbolic tangent +C Eq.2 ii. Based on Eq.2, develop a MATLAB program to compute the velocity for the first 12 seconds of the free falling parachutist with the step size of 2 seconds. Use Eq.2 to derive the terminal velocity when the parachutist is allowed to free fall for an infinitely long time period. Apply a longer time period to the MATLAB program developed in (ii) to find the terminal velocity and then comment the two results. Hint: Find tanh(0) first before using Eq. 2 to calculate the terminal velocity and tanh()1. iv. Apply numerical method to verify the following equation (Eq. 3) for approximating the exact solution of Eq. 2. v(ti.1) = v(t) + 9 = v(t)](t.1-t) Eq.3 v. Based on Eq.3, develop MATLAB programs to compute the velocity for the first 12 seconds of the free falling parachutist with the step size of 2 seconds vi. Compare and comment the results obtained from (ii) and (v) vii. Repeat (v) but reduce the step size to 0.5 seconds viii. Compare and comment the results obtained from (ii) and (vii) ix. Comment the difference in errors between (vi) and (viii) Note: a. All the computed results should be expressed in the form of tables and if appropriate also in the form of graphs: b. Functions should be used wherever possible to simply the program structure and also to allow program codes to be re-used; c. Program testing is an important part of software development. So, it is important to verify the correctness of the developed program; d. Use the print screen' button on the keyboard to capture the MATLAB output display and insert the image into your Microsoft Word report document file to prove that the computed results are actually generated from MATLAB.