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all right so I received my first email request for help on the chapter 11 exercises and specifically the question was with regards to part two of the first exercise and so before even you know look at the problem itself youre the the big challenge with these problems is there just becomes a lot theres a lot to deal with theres a lot to handle okay and so bear with me may take me a little while to get things up and running but just one strategy as you tackle these is you know its meant to kind of be a progression right so you know it says start with our human cannonball problems or 2d trajectory code in which we solve for the optimal launch angle and vacuum right so whats the optimal launch angle well if I know what the launch position is and I know the initial launch velocity Im just going to look at a range of launch angles and my optimal launch angle is going to be the angle that results in the largest distance travel right so if I compute distance traveled as a function of ang