just thinking loud:
(1852*40)/(7*340) = 31 seconds to impact (would be slightly more because an EMRG round slowing in flight, but I don't care right now)
31 seconds, it's 7440 m for the Harpoon AShM (and more for supersonic missiles but I don't want to sound war-mongering
so, at 1852*40+31*240 = 81520 m at the latest! you need to estimate the trajectory of an incoming Harpoon (how will you do it?), and hope that trajectory won't change "abruptly" during the time your EMRG round flies to meet that Harpoon ... wait, 40 nm, so the correction for the curvature of Earth would be quite large
The issue is not just about estimating the incoming trajectory. More advanced cruise missiles are able to maneuver even in terminal flight. As such, EMRG has to retain sufficient kinetic momentum to correct its own trajectory to ensure a kill and the outer limit is estimated to be effective up to 40 nm. Quote from document :
"Now in development, EMRGs that fire GPS-guided or command-guided HVPs at hypersonic
speeds (greater than Mach 5) could intercept threat aircraft and missiles at medium ranges.
These projectiles will have a limited ability to adjust their trajectories to intercept a moving
target. Therefore, the longer a target has to maneuver, the lower the probability an EMRG
round will engage it successfully. For example, an HVP traveling at Mach 7 would take 20 seconds
to reach a Mach 2 cruise missile located 30 nm from the HVP’s launch point. Although
the Navy’s developmental 32-megajoule (MJ) EMRG is capable of firing an HVP about 100 nm
against a surface target, beyond 30–40 nm an unpowered HVP may not be able to adjust its
flight path sufficiently to intercept a maneuvering cruise missile."
