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kuruman
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Introduction
We show how one can solve most, if not all, introductory-level projectile motion problems in one or maybe two lines. To this end, we forgo convention.  We demote clock time ##t## to a parameter of secondary importance and ditch the independence of motion in the vertical and horizontal directions.
Starting from first principles, we develop two primary equations that relate five “basic” parameters to each other: ##\Delta x##, ##\Delta y##, ##v_{0x}##, ##v_{0y}## and ##v_y## (standard definitions).  We view the solution of projectile motion problems as equivalent to solving a system of five equations with the five basic parameters as the five unknowns.  Once the system is solved, the time of flight, if one must have it, is just the ratio ##\Delta x/v_{0x}##.
To sharpen the implementation of the primary equations, we recombine them to derive three auxiliary shortcut equations that facilitate the identification of equation parameters with given variables.  Finally, we...

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