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\begin{equation*}
  \aligned 
  & \dot x(0) \sin\theta_0 - \dot y(0) \cos\theta_0 = 0,
    &\qquad &
    \dot x(T) \sin\theta_f - \dot y(T) \cos\theta_f = 0, \\
  & \dot y(0) \sin\theta_0 + \dot x(0) \cos\theta_0 = v_0,
    &\qquad & 
    \dot y(T) \sin\theta_f + \dot x(T) \cos\theta_f = v_f.
  \endaligned
\end{equation*}
\end{document}