Projectile Motion And Vector:

• Time of flight : $$ T=\frac{2 u \sin \theta}{g}$$

• Horizontal range : $$ R=\frac{u^{2} \sin 2 \theta}{g}$$

• Maximum height : $$ H=\frac{u^{2} \sin ^{2} \theta}{2 g}$$

• Trajectory equation (equation of path) : $$y=x \tan \theta-\frac{g x^{2}}{2 u^{2} \cos ^{2} \theta}=x \tan \theta\left(1-\frac{x}{R}\right)$$

Projection on an inclined plane:

Dot product:

,

A.B = AB $\cos \theta$

Cross product:

A $\times$ B = AB $\sin \theta$

Vernier caliper:

Vernier caliper’s least count = the smallest reading within main scale/ Number of divisions within vernier scale = 1 mm ÷ 10 divisions = 0.1 mm