Range of Projectile formula

The range (Horizontal Range) of a projectile is defined as the horizontal distance between the point it touches the ground and the point of projection. Now, let’s find the Range of the Projectile formula.

Say, an object is thrown with uniform velocity V₀ making an angle θ (theta) with the horizontal (X) axis.

The formula of the range of a projectile is R = (V₀² sin2θ )/ g

The Range formula of a projectile can be derived easily.

If R is the horizontal range covered by a projectile then that means R is the horizontal distance traversed by the projectile after passing the total time of flight T_tot.

Here we will use the horizontal component of the initial velocity only as the effective velocity to traverse this horizontal path.

R = (V₀ cosθ).  T_tot  …………………….. (1)

We will use the equation of the total time of flight now.
T_tot = 2(V₀sinθ )/g …………………..(2)
So, from (1) and (2), we get,
R = (V₀ cosθ). 2(V₀sinθ )/g = (V₀² sin2θ )/ g

So the formula of the horizontal range of a projectile is R = (V₀² sin2θ )/ g