A projectile is fired in a uniform gravitational field (g) with initial speed (v_{0}) and angle (theta_{0})
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A projectile is fired in a uniform gravitational field \(g\) with initial speed \(v_{0}\) and angle \(\theta_{0}\) relative to the horizontal. Note that the Hamiltonian is
\[H=\frac{p_{x}^{2}}{2 m}+\frac{p_{y}^{2}}{2 m}+m g y\]
Find the projectile's motion \(x(t)\) and \(y(t)\) using the Hamilton-Jacobi method.
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