**Projectile Motion **is the form of motion observed when any object is launched into the air. The Projectile motion is subjected to only **acceleration due to gravity.** The object launched is called **Projectile** and its path is called **Trajectory.**

## Formulas

The formulas related to **Projectile Motion** are as follows :

**Time of flight :** T = \( \frac{2u \sin \theta}{g} \)

**Horizontal range :** R = \( \frac{u^{2} \sin 2\theta}{g} \)

**Maximum height :** H = = \( \frac{u^{2} \sin^{2} \theta}{2g} \)

**Trajectory equation (equation of path) :** y = x tan \( \theta – \frac{gx^{2}}{2u^{2}\cos^{2}\theta} \Rightarrow x \tan \theta \left ( 1-\frac{x}{R} \right ) \)

**Projection on an inclined plane**

Up the incline | Down the incline | |

Range | \(\frac{2 u^{2}sin\alpha cos(\alpha + \beta)}{g cos^{2} \beta}\) | \(\frac{2 u^{2}sin\alpha cos(\alpha – \beta)}{g cos^{2} \beta}\) |

Time of flight | \(\frac{2 u sin\alpha}{g cos \beta}\) | \(\frac{2 u sin\alpha}{g cos \beta}\) |

The angle of projection with an inclined plane for maximum range | \(\frac{\pi}{4} – \frac{\beta}{2}\) | \(\frac{\pi}{4} + \frac{\beta}{2}\) |

Maximum range | \(\frac{u^{2}}{g(1+sin \beta)}\) | \(\frac{u^{2}}{g(1-sin \beta)}\) |