Motion in a Plane

Projectile Motion Formulas

For a projectile launched with initial velocity $u$ at angle $\theta$ with horizontal:

1. Equation of Trajectory (Parabolic):

$$y = x\tan\theta - \frac{g x^2}{2u^2\cos^2\theta}$$

1. Time of Flight ($T$):

$$T = \frac{2u\sin\theta}{g}$$

1. Maximum Height ($H_{\text{max}}$):

$$H_{\text{max}} = \frac{u^2\sin^2\theta}{2g}$$

1. Horizontal Range ($R$):

$$R = \frac{u^2\sin 2\theta}{g} \quad (R_{\text{max}} = \frac{u^2}{g} \text{ at } \theta = 45^\circ)$$