Based on extensive Scientific-Wild-Assed-Guessing, that'd be about 2.3 seconds
"Fuck, it. Just shoot it with an RPG."
In all seriousness, it'd be treated just like any other enemy emplacement that's causing problems: hit it with things until it stops being a problem.
They wouldn't stop to think about it or marvel/wonder at how it works, training would ensure they respond to it as they'd respond to a machinegun nest, a sniper or a couple of guys with a rocket launcher: "take it out."
Because this procedure is standard all over the world, the militaries of most nations devote vast amounts of time to making it as hard as possible to determine where the attack is coming from or to make the knowledge irrelevant or out-of-date.
Panzer-Howitzer 2000 - can fire off 5 shells in such a way that they will all land on the target at about the same time (MRSI) and then stow its barrel and bug out of that location before they even hit (leaving whatever's left of the enemy shooting at the place they used to be).
Javelin fire-and-forget rocket that does everything it can to decrease its launch signature and the fire team can bug out instantly after pulling the trigger to avoid counter-attack.
Stealth planes and drones that are so high that you can't detect their presence and are long gone by the time their payload hits.
Weapons that can shoot over fantastic distances to make it harder to return fire and are mobile enough that returned fire is hitting empty ground.
Stealth and "shoot-and-scoot" are the order of the day.
Meanwhile, the "magic reusable bomb" is akin to a pit-and-sandbag machinegun nest from WWII - and just as vulnerable to 5 rounds MRSI of high-explosive artillery or a tank buster bomb.
edited 20th Apr '13 1:18:29 PM by Wolf1066