DYNAMICS

$v_x=v_0\,cos(\theta_0)

$x=\left(\,v_0\,cos(\theta_0)\right)t

$v_y=\pm\, v_0\,sin(\theta_0)-gt

$y=\left(\pm\,v_0\,sin(\theta_0)\right)t-\dfrac{1}{2}gt^2

${v_y}^2=\left(\pm\,v_0\,sin(\theta_0)\right)^2-2gy

$y=x\;tan\theta-\dfrac{1} {2} g\left(\dfrac{x^2} {{V_0} ^2\;cos^2(\theta)} \right)

$s\ =\ r\ \theta$

$v\ =\ r\ \omega$

$a_t\ =\ r\ \alpha$

$a_n\ =\ r\ \omega^2$

$a_n\ =\ \frac{v^2}{r}$

$v_f=v_0\ +at$
${v_f}^2={v_0}^2\ +2\ a\ S$
$S=v_0t\ +\frac{1}{2}a\ t^2\ $

$v\ =\ \frac{ds}{dt}$
$a\ =\ \frac{dv}{dt}$

$Speed\ =\ \frac{Distance\ }{Time}$

$Velocity\ =\ \frac{Displacement\ }{Time}$

$v_{ave}\ =\ \frac{\sum distance}{\sum time}$

$\omega_f\ =\ \omega_0\ +\ \alpha\ t\ $
${\omega_f\ }^2=\ {\omega_0\ }^2\ +\ 2\alpha\ \theta$
$\theta\ =\ \omega_0\ t\ +\ \frac{1}{2}\alpha\ t^2$

$\omega\ =\ \frac{d\theta}{dt}$
$\alpha\ =\ \frac{d\omega}{dt}\ =\ \frac{d^2\theta}{{\rm dt}^2}$

$y_{max}=H\ =\frac{{v_0}^2\ \sin^2\ \left(\theta\right)}{2g}$