User:RyanD1999/sandbox

$$v_{0y}=v_t \sin \theta$$

$$y=\frac{1}{2}gt^2+v_0t+h_0$$

$$y=-\frac{1}{2}g(t^2-\frac{2v_0}{g}t-\frac{2h_0}{g})$$

$$y=-\frac{1}{2}g(t^2-\frac{2v_0}{g}t-\frac{v_{0}^{2}}{g^2})+(\frac{-2h_0}{g}-\frac{v_{0}^{2}}{g^2})$$

$$y=a((x-h)^2+k)$$

$$(h,k)=(\frac{v_0}{g},\frac{-2h_0}{g}-\frac{v_{0}^{2}}{g^2})$$

$$x=v_0t$$

$$v_0=v_t \cos \theta$$

$$y=\frac{gx^2}{2v_{0x}^{2}}+\frac{v_{0y}x}{v_{0x}}+h_0$$

$$y=\frac{gx^2}{2v_{t}^{2} \sin^2 \theta}+\tan \theta \times x+h_0$$