Amonte carlo analysis can be used for optimization. for example, the trajectory of a ball can be computed with 2 |(p14.35) x+yo 2 cos20o y=(tan0o)x where y the height (m), go = the initial angle (radians), the initial velocity (m/s), g 9.81 m/s, and yo vo = 25 m/s, and oo = 50", determine the maximum height and the corresponding x distance (a) analytically with calcu- lus 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 the gravitational constant 1 m, the initial height (m).