"Drop it or I kill the girl!"

I would guess the answer is “it depends”.

Is the gun cocked with a hair trigger? If so then it takes little for the gun to be shot.

Is the gun not cocked and take significant pressure to pull? If so then probably a good chance a head shot will work.

With bombs what if the person has a “dead man’s trigger”? Then don’t shoot.

I would suspect that in most situations, if we assume the shooter can make the head shot cleanly and without hitting the hostage, then taking the shot is the best option. I doubt we can say the chances of the hostage not getting shot are zero but the alternatives are worse.

Lots of ifs in all this though which is why it is a trope in movies. No one can say for certain how it will turn out which puts us on the edge of our seats (the writers hope).

Actually, the classic example is Sam Fuller’s “Forty Guns”.

BAM BAM BAM

“Get a doctor. She’ll live.”

The trope is Put Down Your Gun and Step Away. TV Tropes: Even trained police and military will do this, which goes against every rule and all logic in real life in regards to this situation. …

The main problem with the situation is that the hostage taker, barring the occasional ones who are willing to give their life, doesn’t want to shoot the hostage much more than the heroes do. If they were to kill the hostage because the heroes refused to drop the guns, there is suddenly nothing to keep the heroes from using said guns. However, the characters almost never think this through. Subverted by Shoot the hostage.

Let me make this clear- the cop just does not “take the shot”. But he doesn’t drop his gun, either. Both would be foolish. Once in a great while a trained swat sniper might take that shot.

A couple scenes from movies/games come to mind:

From The Presidio, we have a San Francisco PD detective (played by the same guy who plays Gibbs on NCIS) end up in a standoff with a desperate criminal in a police station, holding a cop hostage with his own gun. The detective is armed with a cup of coffee. A nearby officer has his gun drawn, and the detective instructs him not to drop the weapon under any circumstances.

Basically, he talks the bad guy down by convincing him that the worst thing he could possibly do would be to make the detective spill his coffee (the cup turns out to be empty, BTW).

Meanwhile, in Mass Effect 2, in the DLC “Lair of the Shadow Broker”, Shepard can end up in a hostage situation (with a hostage who has a son, no less) where the solutions include shooting the hostage in the arm “You’ll live”, stalling for time (so his/her partner can smack the bad guy with a telekinetically thrown table), or point out that in the previous game, you either sacrificed the lives of the game’s galactic equivalent of the UN or the lives of thousands of human military personnel to save said space-UN personnel, “So I hope your plan doesn’t hinge on me being unwilling to shoot a damn hostage!”

The latter choice, incidentally, is the “Paragon” or “Light Side” solution. The first one was the “Renegade” or “Dark Side” solution.

Comic variant, at 4:18 of this clip, from the little-known movie The Wrong Guy.

I think it’s just an hypothetical : for some magical reason, the cop’s shot will be 100% accurate, the question being only whether or not the hostage could end up dead nevertheless, due to some reflexive move of the bad guy.

I can’t believe that no one has mentioned the scene in “The Untouchables” at the train station. One of the greatest movies scenes ever! Bad guy is holding the “book keeper” hostage with a gun to his head. Andy Garcia has a pistol trained on the bad guy. Kevin Costner says “You got him?” Garcia replies, “Yeah, I got him.” Costner then says, “Take him.” And Garcia shoots the mafioso through the mouth, leaving the book keeper alive but shaken. I do think that most police SOP does not involve either giving up your gun or shooting the perp in the head though. Most times the police will do everything possible to talk the perp into surrendering first. Shooting the perp in the head is likely the last resort if they feel that the hostage is in iminent danger.

The 1994 Torp hostage crisis was ended by a sharpshooter at 60 metre range. The hostage-taker was squeezed right up to the hostage and holding a gun to her ear, but the bullet entered his temple and exited through just below the ear, ripping through his brain. According to the hostage in a later interview, it was “like he had his power switch flicked off - not a twitch, sigh or tremor until well after he hit the ground.”

I’ve got to clarify this. You’re describing momentum which is conserved. There are force pairs that are equal and opposite but they occur at the same time. IE the force pair when the gun is fired are equal and the force pair when the bullet hits the victim are equal but that doesn’t mean both sets of pairs are equal. (To give an analogy if you hit the brakes as hard as you can on your car at 50 mph the forces generated don’t care if you got up to speed with gentle acceleration or if you gunned it, they’ll be the same no matter how you got up to speed.) Actually you are right the moment change the victim experiences will be less than the shooter. This is in part because part of the “forward” momentum is in the expended gas and the bullet will also dump momentum into the air during it’s forward travel.

For anybody that cares the average force would be given by the follow equation(yes, I know I’m using the simplified versions of these formulas, my physics isn’t what it used to be.)

F =1/2M deltaV^2/D

Where F = average force, M is mass, delta V is velocity change, and D is the distance the change occured over.

Indeed. My point in bringing in the Third law was to demonstrate the absolute theoretical maximum force that a headshot victim might experience (i.e., that of a rifle kick) and note that while it’s enough force to hurt like a bitch, it’s probably not enough to ruin the hostage-taker’s aim if he’s got the barrel of the gun pressed to the hostage’s head. I think we agree here that the actual change of momentum of the hostage-taker’s head is probably not large enough to screw up his aim.

I strongly suspect this is bullshit. In such a situation it tactically is shoot to kill, let alone the difficulty and waste of focus and time to do a leg thing.

Remember, in cases that will be remembered, the US does not kill women and children.

You must have an awfully convenient memory. For some reason, I keep remembering things like My Lai and, for instance, this (although looks like the children were only wounded ): http://www.time.com/time/nation/article/0,8599,1978017,00.html).

I’m afraid you missed the obvious sarcasm, even spelled out via its absurd reasoning in my brief comment on tactics in that post.

Another movie example - in Shooter (starring Mark Wahlberg)

There’s a scene near the end of the movie (Youtube link) where there is a standoff on a snowy mountaintop. Wahlberg (the sniper) arrived early with a friend of his and got into a hidden position with his sniper rifle and a white Ghillie suit. The main Bad Guys arrived in a helicopter, with his girlfriend as a hostage, and also have some of their own snipers hidden on the mountaintop.

The Henchman has a shotgun which he has taped to his hand/arm and is holding it on the girlfriend, stating that if he is shot his last spasms will trigger the shotgun. Wahlberg first takes out the hidden Bad Guy’s snipers. Then he doesn’t shoot the hostage - I think a sniper bullet is too high powered and would do too much damage? He also doesn’t go for a headshot on the Henchman like I assumed he would. Instead he shot Henchman’s shotgun, right near the hand, and destroyed the gun by breaking it in half and mangling what was left of the trigger and the hand taped to it. Then he also shoots off the guy’s entire arm, leaving him screaming in agony - revenge for stuff done earlier in the movie.