## Projectile Motion

• ${v}_{{x}_{i}}={v}_{i}\mathrm{cos}\left(\theta \right)$
• ${v}_{{y}_{i}}={v}_{i}\mathrm{sin}\left(\theta \right)$
• ${v}_{{y}_{f}}={v}_{i}\mathrm{sin}\left(\theta \right)-gt$
• $\theta =\mathrm{arccos}\left(\frac{{v}_{{x}_{i}}}{{v}_{i}}\right)$
• $\theta =\mathrm{arcsin}\left(\frac{{v}_{\mathrm{yi}}}{{v}_{i}}\right)$
• ${x}_{f}={v}_{{x}_{i}}t={v}_{i}t\mathrm{cos}\left(\theta \right)$
• ${y}_{f}={v}_{{y}_{i}}t+\frac{1}{2}{a}_{y}{t}^{2}={v}_{i}t\mathrm{sin}\left(\theta \right)-\frac{1}{2}g{t}^{2}$
• $y=x\mathrm{tan}\left(\theta \right)-\frac{g{x}^{2}}{2{v}_{i}^{2}{\mathrm{cos}}^{2}\left(\theta \right)}$
• ${y}_{\mathrm{max}}=\frac{{v}_{i}^{2}{\mathrm{sin}}^{2}\left(\theta \right)}{2g}$
• $\mathrm{\Delta x}=\frac{{v}_{i}^{2}\mathrm{sin}\left(2\theta \right)}{g}$