Question

Steve applies one of the equations of motion to solve part (c) and finds that he needs to solve a quadratic equation. He writes the following MATLAB script: 1 clc 2 % 3 4 symst f=4.905*t.^2-15.97*t-8.04; t_solution=solve(f==0,t); 5 6 7 8 positive_idx=t_solution>0; positive_t=t_solution positive_idx); sentence1= 'The positive solution is %.2f.\n'; fprintf(sentencel, positive_t); 9 10 11 12 13 negative_idx=-positive_idx; negative_t=t_solution(negative_idx); sentence2='The negative solution is %.2f.\n'; fprintf(sentence2, negative_t); 14 15 The variable t_solution is displayed in the Command Window as: t_solution = 1597/981 - 4127857^(1/2)/981 4127857^(1/2)/981 + 1597/981 1. [2 marks] Briefly explain what symst(line 3) does. II. [2 marks] In line 5, the first input to the solve function uses the == (double equals sign) syntax. Can this be replaced with = (single equals sign)? Briefly explain why or why not. III. [2 marks] In line 4, the element-wise power operator (.^) is used. Is this necessary? Briefly explain why or why not. IV. [4 marks] Briefly explain what line 7 is doing. After line 7 runs, what is the computed value of positive_idx? V. [2 mark] What does the syntax \n used in the fprintf function (lines 9 and 14) mean? VI. [2 mark] What does the syntax %.2f used in the fprintf function (lines 9 and 14) mean? VII. [6 marks] Rewrite lines 7-15 using a for loop and if-else statement. Your code should output the same two sentences as the code above, depending on the sign of the time value being considered.

Answer 1

I. syms is used to dynamically create a variable. Here, syms t is used to create a symbolic variable t and assigns it to a MATLAB variable of the same name.

II. The = operator assigns a value, whereas the == is used to compare the values. = cannot be used in this case. It checks if f==0, using = would assign the value 0 to f.

III.Instead of the element wise power operator .^, power(a,b) can also be used to return the same result. Also just ^ could also be used instead of .^. The element wise power operator is necessary only when matrix values are used. Which is not the case here, so it is not necessary.

IV. t_solution> 0 will find the indices whose values are greater than zero. This value then gets assigned to the index positive_idx