Posts in category 'Algebraic Mechanics'

W.26 Algebraic Physics: Projectile Parabolas, Snell’s Law & Relativity

A Galilean projectile launched from O with initial speed-squared v^2 and elevation spread s traces a parabola whose apex height h = v^2*s/(2*g), horizontal range quadrance Q_range = 16*(v^4/(4*g^2))*s*(1 - s) = (v^4/g^2)*S_2(s), and focus-directrix geometry depend rationally on s; Snell’s refraction law becomes n_1^2 * s_1 = n_2^2 * s_2 in spreads.