Moving-target interception rate ($\dot{N}=\lambda (1-U/v)$)

An ideal one-dimensional stream is emitted at a constant rate $\lambda$, with every projectile moving at the same ground-frame speed v. A target at x(t), moving in the same direction with speed $U<v$, intercepts projectiles emitted at retarded time $s=t-x(t)/v$. Differentiating the count $N=\lambda s$ gives the displayed rate, after the stream's leading edge has arrived. Thus constant emission rate does not imply constant impact rate. Combining this flux with the momentum transferred in each impact gives the mean force on the target.