Question

To prove that : Equation of a projectile is a parabola.

Answer 1

Projectile is the form of the motion that is experienced by the object thrown near the surface of the earth.

The displacement of the object at any time$t$will have both component i.e. x and y

$x=ut\cos \theta$ $\left(1\right)$

$y=ut\sin \theta -\frac{1}{2}g{t}^2$ $\left(2\right)$

The magnitude of the displacement is given as

$\Delta r=\sqrt{x^2+y^2}$

Substitute the value of$t$ from equation$\left(1\right)$in equation$\left(2\right)$we get

$y=\tan \theta \cdot x-\frac{g}{2v_0^2{\cos }^2\theta }\cdot x^2$

Whose generalised form is given as,

$y=ax+b{x}^2$

Hence the equation of the projectile is the parabola.