Jet-area adjustment during ballistic slowing ($A_{\mathrm{hit}}{v}_{\mathrm{hit}}=A_0{u}_0$)

Steady incompressible mass flow rate stays constant along a jet, while speed and cross-sectional area can change under gravity. At a horizontal apex the arriving speed is the initial horizontal component. The force on a target that stops this horizontal momentum is $\dot{m}{v}_{\mathrm{hit}}$, using the conserved nozzle mass flux. Substituting the nozzle area into $\rho A_{\mathrm{hit}}{v}_{\mathrm{hit}}^2$ without adjusting the area gives the wrong result.