Right off the bat, I love The Matrix. It’s one of my all-time favorite sci-fi movies (along with The Animatrix… the sequels suck) and was one of the first films that got me into the genre of sci-fi and still feels very nostalgic to me (I saw it on video when I was twelve).
On the other hand, it is definitely flawed, riddled with plot holes, and the Neo is basically another Jesus Christ inspired main character that countless other sci-fi (and non-sci-fi) films based their basic plot on. But despite its shortcomings, its style, special effects, action scenes, etc. more than make up for the relatively lame story and hole-punctured plot.
But this brings me to one specific scene I’d like to nitpick. It’s nearing the end (spoiler alert) when Trinity momentarily saves Neo from an agent. In spectacular special-effect fashion, Neo dodged the agent’s bullets just as the agent had dodged his by moving his upper body extraordinarily fast while standing still. Walking up to Neo who’s laying on the ground, the agent points his gun at Neo. That’s when Trinity points her gun at the agent’s face and says: “Dodge this” and shoots him in the face (which somehow sends the agent jumping into the air. Uhm hello, conservation of momentum… someone???).
My problem with this, albeit cool scene, is that it makes no sense. Exhibiting the kind of reflexes the agent just showed us, the three seconds that it takes the agent to notice the gun being put to his face and Trinity coolly saying her line should be more than adequate time for the agent to simply move away and shoot her in the face. I mean, It’s cool, but nonsensical.
So here’s my input. A simple calculation to why this doesn’t make sense.
Okay. Let’s say the agent is standing 10-15 m away from Neo (d = 12.5 m ± 2.5 m). When Neo fires at the agent, he lets out 20-24 shots (22 ± 2 shots) in a time-frame of 7 seconds (7.0 ± 0.5 sec). If we are to believe Mythbusters, bullets travel approx. 2500 feet per second or 760 m/s ± (say) 20 m/s. Let’s assume that the time between Neo’s shots is approx. equally divided, i.e. 7 seconds divided by 22 bullets = 0.32 ± 0.04 sec/bullet**. The time it takes Neo’s first bullet to travel the space between Neo and the agent is then the distance divided by velocity of the bullets, i.e. 12,5 m / 760 m/s = 0.016 ± 0.003 sec. This demonstrates the initial reaction time of the agent where he dodges the first bullet. The time elapsed between bullets (0.32 sec) is therefore more than enough for the agent to dodge the previous bullet and anticipate the next one. In summary, the agent dodges a bullet in under 0.016 seconds and has 0.32 seconds to react and dodge the next bullet.
The time it takes Trinity to put her gun to the agent’s face (nota bene, the gun touches his face before she delivers her line) is approx. 2-3 seconds (let’s say 2,5 ± 0,5 sec). In that time the agent could theoretically dodge 2,5 sec / 0.016 sec = 160 ± 40 friggin bullets! I.e. at least over a hundred. Nice one Trinity. Nice one.
Remember kids. If you’re going to play it cool. You are mathematically more likely to die… sooner.
**Uncertainties were performed with a general error propagation formula as described by H. H. Ku.