Multi Formulas + Shapes

Ideal Projectile Motion

r = (v_ocosα)ti + ((v_osinα)t - ½gt²)j

Maximum Height

y_max = (v_osinα)²/g

Flight Time

t = 2v_osinα/g

Range

r = v_o²sin2α/g

Elliptical Paraboloid

x²/a² + y²/b² = z/c

Elliptical Cone

x²/a² + y²/b² = z²/c²

Ellipsoid

x²/a² + y²/b² + z²/c² = 1

Hyperboloid of One Sheet

x²/a² + y²/b² - z²/c² = 1

Hyperboloid of Two Sheets

z²/c² + x²/a² - y²/b² = 1

Hyperbolic Paraboloid

y²/b² - x²/a² = z/c, c > 0