At this point, Sulu turns to face Kirk and deadpans: "Fencing". Like so much else, one might claim the absurdity of Sulu's reply was a joke, and that he wanted to inject a bit of self-deprecating humor into the situation. Forgetting that this reply is likely to further undermine Kirk's already-shaken confidence in his squad's members, this dialogue directly violates the spirit with which Gene Roddenberry imbued his characters: cultural pride. This is why his original first officer was female, why Spock was Vulcan, Chekov was Russion, Uhura was African, and they interacted with the central character from the center of the North American United States. Anyone with an appreciation for the grand history of Japanese martial arts and in particular the near sacred solemnity accruing to swordsmanship would be loathe to mislead a gaijin, insult the ancestors, and demean a ryu by equating bushido to a European sport activity.
Back in the shuttle cockpit, Pike announces "Free jump" and the 3 man team puts on their helmets. "Gentlemen" he continues, as we see an external shot of the shuttle moving away from the Enterprise "we're approaching the drop zone. We have one shot to land on that platform." There is no evidence of that – unless there is no one left aboard the Enterprise who can obey the law of gravity. If the drill is really that important to saving Vulcan, everyone should get aboard escape pods and they should ram the drill, saving the planet and foiling the evil Romulans. Another option would be simply for the Enterprise to fire on the drill. After all, it seems the Narada is unable to detect 3 torpedo-sized projectiles heading to their drill anyway.
We may also note that because the drill is ostensibly jamming all transmissions, any communications between Pike and the suited assault team should be impossible. Not so, apparently. The transmissions seem to work fine. This film never seems able to stick to much of its background information, but here we have Vulcan and Starfleet communications down "because they're being attacked", according to Kirk, indicating this is deliberate jamming – as the advisor informed surrogate Princess Amidala just before the Trade Federation attack. In direct opposition to this, Spock indicated the disruption is a result of the (presumably normal) operation of the Narada's mining drill.
Pike continues on an open transmission: "They may have defenses, so pull your chute as late as possible." Now comes what has to be one of the most ridiculous countdowns in history, as Pike says "Three, two, one" then he decides to switch from acting as captain, team pilot, and future torture victim to impersonating a talking Microsoft Outlook Calendar reminder with "Remember, the Enterprise won't be able to beam you back until you turn off that drill….(pause)… Good luck!" …and he instantly pulls the outer hatch release! What if someone had decided that aborting the countdown gave them time to adjust the seal on a helmet or glove? They would have been spaced! This could have killed them if they were unable to restore the seal in time. It seems the characters could hear the background music which lets the audience know that the drop was coming. The three-man team flies away in a very well executed external CGI shot.
Unfortunately, the physics on this are all wrong because the away team dropped out of a shuttle that was moving toward the Narada, and regardless of how undeserved the generous assumption, we will allow the benefit of the doubt to treat the Narada and Enterprise to be holding station below geosynchronous orbit, but above the atmosphere. Any projectile from the shuttle would follow a trajectory that is roughly parabolic – however the drop team maintains steady distance from the punk snake drill. The only way for this to happen is if the shuttle stopped right next to the Narada unnoticed, hovered over the drill, dropped a commando squad with the entire crew of the Narada oblivious to this, despite their ability to sense precise trajectories across many light years of ships at high warp. Oh, I almost forgot: the Narada would also have to miss the transmissions that the shuttle is successfully broadcasting like a beacon.
In its favor, this segment does have beautiful external CGI, despite the onerous factors shared with the overwhelming majority of segments: not a single woman speaks, and the dialog that does appear is nonsensical, contradictory, and puerile.
We learn a bit more about physics in Star Trek by the Minute 054: Atmospheric Resistance, our next episode.