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## projectile path in 2D is parabolic

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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