= Apex-target condition for a ballistic jet
{title2=$u_y=\sqrt{2gh},\quad u_x=w\sqrt{g/(2h)}$}
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.
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