Derive an expression for the vertical position of a projectile in terms of its horizontal position. This sometimes called parametric equation or path equation for the projectile. I don't know how to get it please help. Thank you.

Answer 1

Y = Vo*sinA*t -(g/2)t^2 and
X = Vo*cosA*t leads to

Y = Vo*sinA*X/(VocosA)
(g/2)*X^2/[Vo^2*cos^2A]
= X*tanA -(g/2)*X^2/[Vo^2*cos^2A]
A is the launch angle and V is the initial velocity.

The equation does not work for a vertical firing, since X = 0 in that case.