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mo Integer vel, No do Roots of Non-linear Equations The upward velocity of a rocket can be computed by the following formula v=un - gt where v is the upward velocity, w is the velocity at which the fuel is expelled relative to the rocket, me is the initial mass of the rocket at time t=0, is the fuel consumption rate and g is the downwards acceleration due to gravity. If # = 2700 m/s, mo= 250,000 kg 9 - 3680 kg/s, and g=9.81 m/s'compute the time tat which v = 2000 m/s. Use single (float) precision (6 significant digits) for all your manual calculations. Use the following methods a) Bisection method (manual calculations, starting points 10 and 50, three iterations, single precision) b) False-position method (manual calc., starting points 10 and 50, three iterations, single precision) c) Secant method (manual calculations, starting points 50 and 40, three iterations, single precision) d) Newton-Raphson (C++ program, use pseudocode, single precision (float), -0.0001,6 -0.01) e) Error analysis (compare a, b, c with d, respectively, express errors in percentage) procedure Newton/...) Newton Raphson p106, p92. Legend: fernal function fis the input function being solved x I derivative off, obtained manually through utt.. analytical derivation x is the starting point of the algorithm 6) relthen nmax is the max number of iterations after which apelul devine the algorithm is aborted (run your program with return different values) em ir / E is desired precision is a limit used to indicate when the derivative becomes almost horizontal otpet. then caputmergence retur caulif end for end procedure Next For questions a, b, and Perform hand calculations Record the answers on the provided Excel file in the shaded boxes Scan the hand calculations Submit the scanned hand calculations in a single file on Avenue For question d) Create a C++ source file with a main program that calls a separate function called "Newton" using the pseudocode shown above Run the program to get the value of the root o Write the value of the root in the shaded box of the provided Excel file Paste in the Excel file a picture of your C++ program output (console): without a picture proof, the answer to C++ question will not be credited Submit the.cpp (not the solution) file on Avenue. For question e) write the errors in the shaded boxes of the Excel file Submit the Excel file on Avenue Note: any assignment that does not include the required C++ program will not be marked - Assignment 2 - Roots of linear equations Do not alter the formatting. Fill only in the shaded areas. Enter data in single precision (6 significa YOUR NAME HERE a f(a) f(b) 10 50 1 BISECTION Step 1 Step 2 Step 3 Root 50 f(a) f(b) 10 2 REGULA FALSI Step 1 Step 2 Step 3 Root f(x0) XO 50 x1 40 f(x1) 3 SECANT Step 1 Step 2 Step 3 Root 4 NR-C++ PROGRAM Root a vs d bvs d cvs d 5 ERRORS Percent value (do not type the % symbol) 6 C++ CONSOLE CAPTURE Picture from your C++ run Place Print Screen of C++ output here Use Alt+PrtScreen to copy