Non-trivial Projectile Problem

Hey everybody — I’ve been busily revising and expanding the first edition of my computer algebra handbooks “wxMaxima for Calculus I” and “wxMaxima for Calculus II”, and I’m enjoying a lot of support from the Maxima community (thanks!). I’m planning to release the next edition in Summer 2016 to address errata, add a code glossary, expand the exercise sets by about 30% and slightly expand the topics covered in the text. In particular, I’ve started to spend a lot of time finding programming solutions to mechanics problems that have no closed-form solution, so Edition 1.1 will be a little more complete on the programming end, in both the Examples and the Exercises.

I spent my afternoon today exploring a projectile launch at 5 m/s from a height of 3 m landing at a height of 0 m. My main interest was to nail down the maximum range and the launch angle corresponding to the maximum range, and this problem actually requires a numerical solution. *find_root* was able to solve the problem, but I also wrote a do-loop to find the maximum range by trial and error — launching the projectile from 10,000 different angles from -90 deg. to +90 deg. and keeping the largest range at each trial using an if-then statement. It strikes me as an excellent lab activity for an introductory mechanics lab for engineering/science students.

Today’s project will likely become the first in a series of monthly articles that I will begin publishing next summer — complete with all the polish you’d expect of a decent blog. For now I’ll continue working on my final revisions to the books, and I’ll just post an attractive visualization of the numerical method for your amusement:

maxout_5632_7

Thanks for your support!

Zak

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