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 !

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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 ax is zero. The position of the object at any time t is given by,

Here, x0 = 0, ux = u cos θ, ax = 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 ay 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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