PART B: ATTEMPT ALL QUESTIONS Question B1 (15 marks) The velocity of a rocket can be computed using the following formula: V = u In - 1-gt mo -96) where u is the velocity of the exhaust gas, mo is the initial mass is the fuel consumption ratet is time and is the acceleration due to gravity. This equation is explicit for the velocity, v. However, if we need to find the time at which the velocity reaches a desired value, the equation is implicit in time, a) If -2000 ms. mo-200,000 kg, -2,500 kg sand g-9.81 ms. rewrite this equation in a way that the time at which the rocket reaches 800 ms can be found using a root finding method (i.e. f(t)-o). Replace the symbols in the equation with the values given above. Write a MATLAB function handle for ft). b) Use the Method of False Position to calculate the time at which the speed of the rocket is 800 ms. Your precision should be 0.1 ms and you are told that the root lies between yo and 40 seconds. Fill in the details of each iteration in the table below - provide 3 decimal places. You may need more or less rows. (Note: workings are not required) Lower limit t U pper limit, tu (0) Estimated Root, tr Iteration Number 1 30 40 time (to the nearest o.1 second) = Page 9 of 2 ENG1060 Computing for Engineers in your reasoning in c) Circle True or False for the following statements below and briefly explain your re the space provided. i. The Newton-Raphson method is guaranteed to converge more rapidly for problems like the one in the part (a). TRUE / FALSE ii. For a given precision, the Newton-Raphson method and the method of false position will converge to the same estimate of the root. TRUE / FALSE iii. The bisection method is unlikely to converge for this problem even if the root is bracketed TRUE / FALSE