B recall the liquid surge vessel problem we solved in

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b. Recall the liquid surge vessel problem we solved in discussion. Now, the inlet and outlet flow rates are not constant. Instead, they are functions of time and height, such that ( ) and . Use ode45 to solve the differential equation and plot the height as a function of time (between 0 and 50). The initial height is 1 m and the area of the tank is 5 m 2 . c. Consider the following reaction: i. Derive the rate equation for each species. ii. In MATLAB, create a function m-file to evaluate the rate equations you derived. Use ode45 to solve for the concentrations of each species. Plot each concentration as a function of time from t = 0 to t = 10 min. Assume that k 1 = 0.5 L/mol · min, k 2 = 2 L/mol · min, and k 3 = 1 min -1 . The initial concentrations of A and B are 1 mol/L and 5 mol/L, respectively. 4. (8 points) You’re driving up to Lake Tahoe to go skiing; however, on the way, a deer jumps in front of your car and you swerve to avoid it, but end up hitting the guard rail. The guard rail is designed such that the force that the rail applies to the car is a function of the velocity v and the displacement x of the front edge of the rail according to the equation: ( ) where K = 30 s-kg/m 5 is a constant.
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Your car has a mass of 1250 kg and hits the guard rail at a speed of 60 mph. Determine and plot the velocity of the car (in m/s) as a function of its position for 0 x 5 m.
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  • Spring '14
  • Derivative, Invertible matrix, Computer algebra system, Guard rail

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