Question

Can you prove that path of a projectile is a parabola....???

Answer 1

the equation of the trajectory of a projectile motion is a complex equation of a parabola

Answer 2

consider a body projected with a speed (u) , making an angle theta(¤)with the horizontal,
let at any instant the body reaches the point P,
by covering the horizontal distance x and vertical distance y in time t :

For horizontal motion:
horiz. distance(x) = horiz. speed×time
= ucos¤ × t
•°• t = x/ ucos¤
For vertical motion :
y = ut - 1/2 g(t×t)
y = usin¤ × x / ucos¤ - 1/2 g × (x×x) / (u×u) × (cos×cos)¤
y = xtan¤ - g× (x×x) / 2 (u×u) (cos×cos)¤
hence, projectile motion is parabolic