Translations:Raypath for velocity linear with depth/3/en

Let a particle of energy start at the origin $\left(x{\rm {=0,\ }}y{\rm {=0}}\right)$, where the path makes at an initial angle ${\theta }_{0}$ with the vertical. The particle travels along a circular arc to point $\left(x{\rm {,\ }}y\right)$, where the path makes an angle $\theta$ with the vertical. We wish to find the coordinates $\left(x{\rm {,\ }}y\right)$. The horizontal distance is given by