The geometry of fireworks

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It’s a fun little basic calculus problem to calculate the size of the parabolic envelope. Here’s a Project Euler challenge about it, if anyone feels up to it. Project Euler problems are usually problems you have to use computer programs to solve, but this one is readily solvable with pen and paper using some elementary calculus (hint: solve it in 2D, then calculate the solid of revolution). It’s trickier than calculus problems you solve in high school, but not much more so, it just requires a good understanding of derivatives and integrals (edit: some knowledge of trigonometric identities is also helpful).

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