Physics Derivation Graph navigation Sign in

projectile path in 2D is parabolic

Generated by the Physics Derivation Graph.

Using the 2D equations of motion, show that projectile path is second order polynomial of the form y = a x^2 + b x + c

Eq. \ref{eq:4718749} is an initial equation. \begin{equation} v_{0, x} t = x - x_0 \label{eq:4718749} \end{equation} Divide both sides of Eq. \ref{eq:4718749} by \(v_{0, x}\); yields Eq. \ref{eq:8858248}. \begin{equation} t = \frac{x - x_0}{v_{0, x}} \label{eq:8858248} \end{equation} Eq. \ref{eq:5756391} is an initial equation. \begin{equation} y = - \frac{1}{2} g t^2 + v_{0, y} t + y_0 \label{eq:5756391} \end{equation} Substitute LHS of Eq. \ref{eq:8858248} into Eq. \ref{eq:5756391}; yields Eq. \ref{eq:9683207}. \begin{equation} y = - \frac{1}{2} g \left( \frac{x - x_0}{v_{0, x}} \right)^2 + v_{0, y} \frac{x - x_0}{v_{0, x}} + y_0 \label{eq:9683207} \end{equation} Eq. \ref{eq:9683207} is one of the final equations. expression is a second order polynomial; projecticle motion is parabolic