Question

1. Velocity of a rocket is given as a function of time in table 1. Table 1. ind any 2l order polynomial of Lagrangian interpolation from the table 1 by 0 10 15 b) Build a program in Matlab for the Lagrangian polynomial interpolation to: 227.04 362.78 20 517.35 bl) Determine the value of the velocity at 16s using formulas of the 1" order and the 4th order Lagrangian polynomial interpolation. From that, find relative error between these two results b2 Using the 3d order polynomial interpolation for velocity, build a program 22.5602.97 b3) Using the 3d order polynomial interpol in Matlab to find acceleration of the rocket at t 12 s. ation for velocity, build a programm 30 901.67

Answer 1

Given that t(sec) v(m/s) 10 227.04 15 362.78 20 517.35 22.5 602.97 30 901.67 In Newton's divided difference interpolation, there are different methods of interpolation such as 1) linear interpolation 2) Quadratic interpolation 3) 3^rd order interpolation 4) General n^th order interpolation Since in Question it is not specified which interpolation to be used, the following answer given on linear interpolation. rightarrow each interpolation techniques gives approximate values only rightarrow linear interpolation uses two set of values i.e (x_0, y_0) and (x_1, y_1) \r\n the general formula for linear interpolation is f_1(x) = b_0 + b_1(x - x_0) where f_1(x) rightarrow linear interpolant of function f(x) = y b_0 = f(x_0) b_1 = f(x_1) - f(x_0)/x_1 - x_0 Here in question the function is velocity, which can be written as v(t) [function of time] and the two set of point are (to, v(to)), (t_1, v(t_1)) since we need to find velocity at t = 16 sec we will choose t = 15 t_1 = 20 v(t_0) = 362.78 v(t_1) = 517.35

Answer 2

Given that t(sec) v(m/s) 10 227.04 15 362.78 20 517.35 22.5 602.97 30 901.67 In Newton's divided difference interpolation, there are different methods of interpolation such as 1) linear interpolation 2) Quadratic interpolation 3) 3^rd order interpolation 4) General n^th order interpolation Since in Question it is not specified which interpolation to be used, the following answer given on linear interpolation. rightarrow each interpolation techniques gives approximate values only rightarrow linear interpolation uses two set of values i.e (x_0, y_0) and (x_1, y_1) \r\n the general formula for linear interpolation is f_1(x) = b_0 + b_1(x - x_0) where f_1(x) rightarrow linear interpolant of function f(x) = y b_0 = f(x_0) b_1 = f(x_1) - f(x_0)/x_1 - x_0 Here in question the function is velocity, which can be written as v(t) [function of time] and the two set of point are (to, v(to)), (t_1, v(t_1)) since we need to find velocity at t = 16 sec we will choose t = 15 t_1 = 20 v(t_0) = 362.78 v(t_1) = 517.35