Projectile motion

Projectile Motion

$v_{x_{i}} = v_{i} \cos (θ)$
$v_{y_{i}} = v_{i} \sin (θ)$
$v_{y_{f}} = v_{i} \sin (θ) - g t$
$θ = \arccos (\frac{v_{x_{i}}}{v_{i}})$
$θ = \arcsin (\frac{v_{yi}}{v_{i}})$
$x_{f} = v_{x_{i}} t = v_{i} t \cos (θ)$
$y_{f} = v_{y_{i}} t + \frac{1}{2} a_{y} t^{2} = v_{i} t \sin (θ) - \frac{1}{2} g t^{2}$
$y = x \tan (θ) - \frac{g x^{2}}{2 v_{i}^{2} \cos^{2} (θ)}$
$y_{\max} = \frac{v_{i}^{2} \sin^{2} (θ)}{2 g}$
$Δx = \frac{v_{i}^{2} \sin (2 θ)}{g}$