FormulaHorizontal throw (throw distance, initial velocity, initial height) $$ w ~=~ v_0 \, \sqrt{ \frac{2\, y_0}{ g } } $$
FormulaHorizontal throw (throw duration, initial height) $$ t_{\text d} ~=~ \sqrt{ \frac{2\, y_0}{ g } } $$
Exercise with solutionLevel 4 (for very advanced students)Torsion tensor & Christoffel symbols with torsion In this problem (with solution) you have to derive the torsion tensor and then the expression for Christoffel symbols with torsion.
FormulaCoriolis force - magnitude (velocity and angular velocity orthogonal) $$ \class{green}{F_{\text c}} ~=~ 2m \, \class{red}{v} \, \class{brown}{\omega} $$
FormulaCoriolis force (+ direction) $$ \class{green}{\boldsymbol{F}_{\text c}} ~=~ 2m \, \left( \class{red}{\boldsymbol{v}} ~\times~ \class{brown}{\boldsymbol{\omega}} \right) $$
FormulaCoriolis acceleration (velocity, angle) $$ \class{green}{a_{\text c}} ~=~ 2 \, \class{red}{v} \, \class{brown}{\omega} \, \sin(\varphi) $$
FormulaArchimedes principle (Buoyancy force, Density, Volume) $$ F_{\text A} ~=~ \class{blue}{\rho} \, \class{red}{V} \, g $$
