Formulas of Projectile Motion

From the graphical diagram of the projectile motion, the formulas of projectile motion are derived as follows. We have previously discussed the definition of projectile motion. The study of projectile motion is often featured in school physics where many projectile motion problems are tested. There are many ways to study projectile motion in physics. Knowing the formulas for projectile motion and the projectile motion equations help tremendously when solving any projectile motion problems. The analysis below comes from many projectile motion problems and results of projectile motion activities. The results are gathered and developed as physics notes on projectile motion problems.

Deriving formulas of projectile motion

Let x denote the horizontal projectile motion or the horizontal component of displacement of the projectile motion.

Let y denote the vertical projectile motion or the vertical component of displacement of the projectile motion.

The horizontal projectile motion is analyzed separately from the vertical projectile motion.

Horizontal projectile motion	Vertical projectile motion
Initial velocity = u cos A	Initial velocity = u sin A
Acceleration = 0	Acceleration = - g (g = gravity)
Time taken = t	Time taken = t
Distance moved = x	Distance moved = y
x = ut cos A	y = (ut sin A) - ½ gt2
Final speed vx = u cos A	Final speed vy = (u sin A) - gt

The horizontal velocity v_x remains constant but the vertical velocity v_y decreases steadily from its initial value at a rate of g (gravity).

More projectile motion equations

The magnitudes of the displacement and the velocity after time t are given by:

Displacement magnitude (distance)

Velocity magnitude (speed)