A rocket has an initial mass of 1500 kg, in where 80% of this mass compromises of fuel. The rocket burns fuel at a certa

[answerhappygod]

A Rocket Has An Initial Mass Of 1500 Kg In Where 80 Of This Mass Compromises Of Fuel The Rocket Burns Fuel At A Certa 1 (36.69 KiB) Viewed 37 times

A rocket has an initial mass of 1500 kg, in where 80% of this mass compromises of fuel. The rocket burns fuel at a certain rate such that a constant thrust of T = 36000 N is produced. Figure 1 demonstrates the forces acting on a rocket during take-off. Fo Figure 1: Rocket During Take-off. After takeoff, the mass of the rocket, m, reduces with time t at a rate defined by equation (1). m = 1500 - 40t m At the same time, the rocket also experiences a drag for of FD = 0.02G d²y dt² y 2 Where F, is the drag force experienced by the rocket, is the vertical velocity of the rocket and G = 9.81 ms². Using Newtons law, the equation of motion for the rocket can be expressed as = T-mG-FD (1) (2) (3)
1. Based on equations (1), (2) and (3), i) ii) i) 2. Based on the differential equations and initial conditions derived from Question 1, Suggest four methods you can use to solve for y numerically. Among these methods, select the most accurate one and explain why it is the most accurate. Based on your selected method in i), explain in detail and in your own words, all the steps required to implement the said method to solve the problem in Question 1 (Calculation is NOT required for this question). ii) Rewrite equation (3) in terms of and t only. Hence, convert the equation into two first order differential equations. How many initial conditions are required to solve the two differential equations in i)? State the initial conditions. 3. Using ONLY MATLAB or OCTAVE as your programming platform, i) ii) ii) Explain the algorithm you will apply in your programming platform to implement the chosen numerical method from Question 2. (NO code is required for this question). Develop a flowchart based on your algorithm and explain the flowchart. (NO code required for this question. You may want to refer to your SEMM/SKMM 1013 notes for this question). Develop a SINGLE script of code in your programming platform to solve for y from t = 0 s to t = 10 s using a step size of h = 1. (Please fully comment your code and display the output of your code in graphical form by plotting y against t for 0 ≤t ≤ 10. Make sure to label and explain your plot. Paste your code inside the report. DO NOT screenshot your code for the report. Make sure that your code reflects the flowchart, algorithm and steps that you have given). 4. Based on your answer in Question 3, i) Given that the exact solution for y at t = 10 s is 800.2015 m. Verify your results in Question 3 by calculating the percentage error and explain the significance of the error. What can you conclude from the chosen numerical method in Question 2? What improvements can be made in Question 3 to increase the accuracy of your results?