 Apex-target condition for a ballistic jet

For a jet arriving horizontally at a target displaced horizontally by w and upward by h, the target lies at the projectile apex. Vertical kinematics gives $u_y^2=2gh$ and flight time $u_y/g$; the horizontal travel then fixes the displayed $u_x$. The launch speed is $\sqrt{u_x^2+u_y^2}$ and $\tan \theta =2h/w$. The ideal ballistic approximation neglects air drag, breakup and internal jet stresses after launch.