If a projectile is projected at an angle 0 from the horizontal with velocity u under the gravitational field of the earth, prove that the path of the projectile will be a parabola !

Projectile Given Angular Projection

• Equation of path of projectile − Suppose at any time t, the object is at point P (x, y).

For motion along horizontal direction, the acceleration a_x is zero. The position of the object at any time t is given by,

Here, x₀ = 0, u_x = u cos θ, a_x = 0
[Velocity of an object in the horizontal direction is constant]
Putting these values in equation (i),

⇒ x = ut cos θ
⇒
For motion along vertical direction, the acceleration a_y is −g.
The position of the object at any time t along the vertical direction is given by,

Here,

∴
Putting the value of t from equation (ii),

⇒

This is an equation of a parabola. Hence, the path of the projectile is a parabola.