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# A Monte Carlo analysis can be used for optimization. For example, the trajectory of a ISBN: 9780073401102 336

## Solution for problem 14.35 Chapter 14

Applied Numerical Methods W/MATLAB: for Engineers & Scientists | 3rd Edition

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Problem 14.35

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.

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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,...

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##### ISBN: 9780073401102

This textbook survival guide was created for the textbook: Applied Numerical Methods W/MATLAB: for Engineers & Scientists , edition: 3. Applied Numerical Methods W/MATLAB: for Engineers & Scientists was written by and is associated to the ISBN: 9780073401102. The answer to “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.” is broken down into a number of easy to follow steps, and 147 words. The full step-by-step solution to problem: 14.35 from chapter: 14 was answered by , our top Engineering and Tech solution expert on 03/05/18, 09:01PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 24 chapters, and 496 solutions. Since the solution to 14.35 from 14 chapter was answered, more than 252 students have viewed the full step-by-step answer.

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