A Monte Carlo analysis can be used for optimization. For example, the trajectory of a

Chapter 14, Problem 14.35

(choose chapter or problem)

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.