# 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*).

*a*

_{x}is zero. The position of the object at any time

*t*is given by,

Here,

*x*

_{0}= 0,

*u*

_{x}=

*u*cos

*Î¸*,

*a*

_{x}= 0

[Velocity of an object in the horizontal direction is constant]

Putting these values in equation (i),

⇒

*x*=

*ut*cos

*Î¸*

⇒

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.**

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