A Monte Carlo analysis can be used for optimization. For example, the trajectory of a ball can be computed with y = (tan0)x g 2v2 0 cos20 x2 + y0 (P14.35) where y = the height (m), 0 = the initial angle (radians), v0 = the initial velocity (m/s), g = the gravitational constant = 9.81 m/s2 , and y0 = the initial height (m). Given y0 = 1 m, v0 = 25 m/s, and 0 = 50o , determine the maximum height and the corresponding x distance (a) analytically with calculus and (b) numerically with Monte Carlo simulation. For the latter, develop a script that generates a vector of 10,000 uniformly-distributed values of x between 0 and 60 m. Use this vector and Eq. P14.35 to generate a vector of heights. Then, employ the max function to determine the maximum height and the associated x distance.

Day 5 fprintfThis function is used to format output anything written in single parentheses that becomes a string of text is a string value, or a numerical value see picture below to see the syntax). Example: >> y=input('Enter a number') Enter a number Or >> z = input('Enter Text:','s') Enter Text: Syntax:fprintf(format_string,...