Projectile Motion & Vectors Formulas

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.


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

projection on an inclined plane
Up the inclineDown 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\(\frac{u^{2}}{g(1+sin \beta)}\)\(\frac{u^{2}}{g(1-sin \beta)}\)
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