show that path of a projectile is a parabola.

Suppose a projectile of mass ‘m’ is projected with velocity ‘u’ at an angle θ with the ground.

The horizontal component of the initial velocity is, u= u cosθ [this remains constant]

The horizontal displacement at any time ‘t’ is, X = ut = ut cosθ

=> t = X/(u cosθ)

The vertical component is given by, u= u sinθ

The vertical displacement at any time ‘t’ is, Y = ut – ½ gt = ut sinθ – ½ gt2

=> Y = u[X/(u cosθ)]sinθ – ½ g[X/(u cosθ)]2

=> Y = X tanθ – gX/[2ucosθ]

Which is the equation of a parabola. So, the path of the projectile is parabolic.

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