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kuruman
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Introduction
In a homework thread a while back a PF member expressed dismay along the lines of “oh no, not another boring projectile motion problem.” Admittedly, I shared the member’s sentiments at the time.  Yet after some thought, I concluded that it is the unvarying recommended strategy of the genre that makes it boring: (a) Write down the  SUVAT equations ada[ted for projectile motion; (b) find the time of flight from the vertical motion equation; (c) use the time of flight to find whatever else you need. “Perhaps,” I thought, “relief from ennui might be found if one forsakes the traditional approach altogether.  How about a formulation of projectile motion based on geometry and trigonometry that allows analysis without quadratic equations?” This tutorial is a streamlined account of how to do it.
The velocity triangle
In 2-d projectile motion without air resistance the equation relating the velocity ##\vec v_{\!f}## at time ##t_{\!f}## and the initial velocity ##\vec v_0##  is...
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