Formulas and Concepts of Projectile Motion

The projectile motion is divided into two parts: a horizontal motion with no acceleration and a vertical motion with constant acceleration due to gravity.

Consider the following example of a ball being launched at an angle from point O to the horizontal x-axis with an initial velocity of u:

(Image will be uploaded soon)

• Point O is defined as the point of projection.
• θ is defined as the angle of projection and
• OB = Horizontal Range.
• H is defined as the height of the particle.
• The time of flight refers to the amount of time it takes a particle to travel from point A to point B.

Differential equations of motion can be used to discover various projectile motion parameters.

The linear equation of motion is:

v = u + at

S = ut + 1/2(at²)

v² = u² + 2aS

Apply the above equation for projectile motion, the equation will now be,

v = u – gt

S = ut – 1/2(gt²)

v² = u² – 2gS

Here,

u = initial velocity

v = Final velocity

g = Acceleration due to gravity (Taking it negative because gravity always work downward)

S = Displacement

t = Time