Variable Terminal Velocity

"How fast you fall depends on who and what you are."

The wacky world of TV physics seems to postulate, among other factors, that how fast a person or object is pulled towards the ground is a function of how heroic they are, and not the constant acceleration of gravity (9.8 meters/second2) that the rest of us have to deal with.

For instance, no matter how tall a cliff or building is, should a character or a fragile vase fall off, there will always be enough time for the Hero to leap after them, catch up to them in mid-fall, and rescue them.

This is a gross violation of physics in most cases. One object accelerated by gravity alone cannot pass another such object that was dropped before it. Neither the size of the objects nor the relative virtues of them can change that. Galileo and Newton both famously showed this, and Dave Scott confirmed it much later in a near-perfect vacuum.

It is possible for this to work to a limited extent if you factor in air resistance against the falling object. But even then, you'd need to fall a very long distance (as in thousands of feet while skydiving, not the hundreds of feet out an apartment window) for this effect to be workable in your favor. And you also have to make sure the wind resistance is, in fact, in the rescuer's favor (by, say, falling forward and keeping your arms and legs together as the rescuer while the person in danger is falling flat with their limbs hanging out).

It only gets worse if the falling rescuing hero completes the rescue with help of Building Swing gadgetry like grappling hooks or ropes: in Real Life, a falling person trying that would be more likely to lose the rope than save the person on the other end.

Rescuing heroes are not the only things to be affected by variable terminal velocity, mind you. In some genres, everything falls faster than an anvil.

A common variant involves somebody skydiving without a parachute, catching up with something that will save them (a parachute, an opponent with a parachute, an aircraft!) in the nick of time (sometimes even racing for it with someone else), and surviving. Interestingly enough, this could actually work - someone falling with a parachute will tend to fall in the "boxman" position, spread-eagle with their belly towards the ground, and may remain that way for some time before deploying the chute. If someone else left the plane shortly after them and fell with their arms and legs tucked against their body, face towards the ground, then they would have a much higher terminal velocity, and could catch up with the would-be parachutist... though pity them if they miss their target and must now contend with falling towards the Earth with no means of slowing their descent. This was confirmed by the MythBusters when they took on the movie Point Break, although it was determined that both men would have to jump from a much greater altitude than they did in the movie in order to have enough time to make it work. And it actually happened in the case of a particular skydiving incident mentioned in the Real Life section below.

See also Not the Fall That Kills You.

Anime and Manga

 * A similar situation occurs in Mai-Otome when Arika and Mashiro are stuck in a cave with lava that's only dangerous if you touch it. Judging by the height of the ceiling they fell from, there was simply not enough time for Mashiro to unlock Arika's powers and for Arika to say "Materialize".
 * In Blood Plus, Hagi jumped off a building and manifested his chiropteran powers (wings) in mid-fall to catch Saya.
 * In one of the final episodes of Noein, Haruka leaped off an insanely tall pillar to rescue a falling Yuu. Her ability to make the rules of space/time sit down and shut up may have had an impact on her ability to catch up to him.
 * The "catching up with a falling person" happens in the finale of Sailor Moon Super S, but the distances involved (starting from a magically floating ruin that's gradually ascending into the upper atmosphere) make it somewhat plausible.
 * Usagi transforming into Princess Serenity, flowing gown and all, really helped her speed up to catch Chibi.
 * The first episode of Mezzo DSA has a really egregious example. Mikura has to take a rope to escape from the top floor of a building, but she also has a little girl to protect and bad guys to fend off. Solution? She chucks the girl out the window, slides down the rope (slower than falling), and gets outside just in time to catch the girl. Uh huh.
 * Minor subversion by Great Teacher Onizuka. In one episode, Kanzaki trapped Onizuka into inadvertently pushing her off a rooftop. Being who he is, Onizuka then proceeded to run straight DOWN THE WALL of said building, catch her in her fall and take the impact for her. He survived.
 * Subverted similarly when he saves Noboru when he was Driven to Suicide--twice—by diving off into him, catching him in midair, then absorbing the full force of the impact himself.
 * In one of the Appleseed movies Deunan makes her dramatic exit by jumping out of a really tall building and apparently has her companions throw her 4m tall powered armor after her. She spreads out her arms and legs and lets the open suit land on her, seals the front hatch, and fires the jetpack about 2m before hitting the water below her. For no apparent reason, there was no hurry at all.
 * In another scene she has her powered armor crash into an enemy in mid air and saves herself by jumping out just before the impact. Breareos and Thereos still have some time to chat and make plans what they have to do and then decide who should catch her. It's not the least plausible part of the film.
 * In Final Fantasy VII: Advent Child Cloud and Sephiroth spend almost the entire final battle in mid air. Apparently terminal velocity can be reduced to almost nothing.
 * Sephiroth can actually fly, and Cloud was always, somehow, lifted by the strength of Sephiroth's blows. A better example occurs earlier, when Rufus and Kadaj are on the top of a building.
 * Used bizarrely in Fairy Tail, when Natsu and Wendy are knocked out of the air on the same time, and Natsu hits the ground early enough before Wendy that he was able to crawl across it and catch her.
 * In the climax of Ranma ½'s long-running "Ranma and Nodoka" story arc, Ranma's mother goes flying off a cliff overlooking the ocean when Genma, who was carrying her, crashes into a tree. Ranma immediately springboards off the top of his father's head after her --repeat, springboards off the top of Genma's head, adding height to his leap when Nodoka is already plunging down. Although the cliff is, at best, a hundred feet high (Genma comes down via rope a few instants later) Ranma has enough time to a) somehow catch up to Nodoka, b) cradle her very gently in his arms, c) grab her sword and toss it at the cliffside further down, creating a foothold, and d) touch down on the sword very lightly. All while side characters gasp and comment on his actions, more worried that the water will reveal Ranma's secret to his mother than about either of them splatting on the cliff OR the water.

Film

 * It was partially inverted in the film Spider-Man 3, when Spidey pursued a plummeting Gwen Stacy. The reason he is able to catch up to her is that his super agility and wall crawling powers allows him to land on various falling rubble and use them as jumping platforms to accelerate himself to reach her.
 * Averted even more later on when he has the power of the Green Goblin's flier to accelerate him faster than gravity would.
 * But done straight in the first movie, where Spidey is able to grab Mary Jane after the Green Goblin drops her and a tram car. Despite said Jane and car being dropped at least a couple seconds before he goes after them.
 * The car had a long cable that took longer to leave the bridge than Spidey, so that part makes sense.
 * Seen as a complaint in the opening scene from The Two Towers when Gandalf uses the "reduced air resistance" trick catches up to his sword (which had an inconsistent profile, tumbling as it was), and accelerates further to take on the balrog, which is a huge thing with lots of surface area and wings. On top of that, of course, Gandalf is an incognito angelic being, and in a film series with rings that cause invisibility, ghosts, giant fiery eyes, fire demons and elves one would think that people wouldn't be overly concerned about a plot-driven reason to tweak the laws of gravity, but there you are.
 * So, basically, what you're saying, is that A Wizard Did It?
 * Also, one wonders if the fiery pits of the Balrog might not cause something of an updraft.
 * He's a friggin' Maiar! They invented the laws of physics (well, the Valar did, Ea's influence non-withstanding). Nuff said.
 * I still vote for A Wizard Did It.
 * In the opening sequence of GoldenEye, James Bond drives a motorcycle over a cliff and catches a falling airplane with enough time to right it before it hits the ground.
 * Truth in Television to some extent. The stuntman concerned actually skydived into the plane in the air. The plane wasn't unpowered, though, and a falling human would probably have a higher terminal velocity than a powered plane in flight position, what with, y'know, wings and all.
 * In the earlier James Bond film Moonraker Bond is thrown out of a plane without a parachute and uses the tucked position in order to catch up with the pilot, who had bailed out earlier and was falling in the boxman position. Bond overpowers him and steals the parachute. Before he can equip it properly though, Jaws catches up with Bond and Bond only escapes being bitten by deploying his parachute in the nick of time, slowing him enough that Jaws plummets away. All of that is reasonably accurate, although they were falling for long enough that they must have started above 25,000 feet, which would require oxygen equipment. However, when Bond detaches the parachute from the pilot, the pilot starts falling faster than Bond for no apparent reason.
 * In the Brazilian movie Simão, o Fantasma Trapalhão, a clumsy man lets a wristwatch falls off a balcony, goes down the stairs and catches the watch before it hits ground. His explanation? "The clock was 5 minutes late".
 * Possibly the most egregious example: In Charlie's Angels: Full Throttle, an attack helicopter is set onto a flatbed truck with its rotors locked for transport. The truck crashes and the chopper falls off a dam. The three characters are able to dive off the dam, catch the helicopter, unlock the rotors, spin up the engine, and fly away before it hits the ground.
 * Averted in The Incredibles when Elastigirl and her kids drop out of the airplane. All three fall at the same rate.
 * In The Dark Knight, Rachel Dawes is dropped out a window by the Joker, and Batman jumps out several seconds later to catch her. While her fall is slowed by a slanted wall directly beneath the window, Batman slides along the same wall, so his fall should have been likewise slowed. Finally, he saves her by flipping her so that she lands on him, regardless of the fact that the momentum change would still be enough to break most of her bones.
 * Averted in I Robot when Sonny goes to save Dr. Calvin from falling to her death. He is clearly shown propelling himself downwards towards her by pushing off from a metal railing, which explains why he falls faster.

Literature

 * As their ability to fly fails in The Hitchhiker's Guide to the Galaxy, Arthur Dent realizes that he can't catch his falling girlfriend, because gravity doesn't work that way. He then realizes, physics be damned, that he was just flying a moment ago, and he'll damn well fall faster to catch up to her.
 * Bella Swan in New Moon jumps off a hundred-foot-cliff during a thunderstorm, backflops onto a rocky ocean with an undertow, nearly drowns...and suffers no injuries. It's worth noting that the Mythbusters once tested to see if disrupting surface tension of water would cushion the fall and dropped their test dummy Buster from a crane onto the ocean from a lesser height on a calm day. Backflopping Buster ended up shattering from the sheer force of hitting the ocean and losing one leg.
 * In the Iain Banks novel Look to Windward a character visiting an Airsphere (an air filled force field in space about 300,000 km across!) drops his pen and jumps after it, trying at first to catch it by freefalling but giving up and using powered thrust to overtake it. His hat on the other hand that blew off on the way down he decides he can get it on the way back up.

Live Action TV

 * In Pretty Guardian Sailor Moon, Ami triggers her first transformation into Sailor Mercury while falling from a third-floor balcony—but the invocation of the change takes several seconds longer than it realistically would have taken her to fall. (Not the change itself, which is presumed to be instantaneous given evidence elsewhere in the series, but the hand gestures and the spoken words that set it off.)
 * Buffy the Vampire Slayer really went overboard with this one. Evil monster jumps into a hole to kill itself and trigger the end of the world. Buffy had time to run to her boyfriend, tell him her plan, grab a line from him, run back to the hole, and jump in, dragging her line over the cliff edge. Did she make it? Well, we're still here, aren't we?
 * A Red Dwarf episode had Ace Rimmer jump out of an exploding plane and air-surf a crocodile down to a baddie who had parachuted out before him.
 * What a guy.
 * Oh, also; after Ace steals the parachute, parachutes to the ground, rescues the princess, takes off on a flying motorcycle, and skywrites "Smoke Me A Kipper, I'll Be Back For Breakfast", the guards watching all of that have time to add this exchange: "He got away! I can't believe he got away!" "That was Ace Rimmer! We are lucky to be alive!" before the crocodile finally hits the ground - landing on top of them, naturally.

Other

 * The "plot" of the Tower of Terror ride at Disney's Hollywood (ne MGM) Studios is that you're stuck in a malfunctioning elevator that rises and drops however it pleases...the reality, however, is that the elevator car is on a belt, which means that you can very well be hurled downwards faster than the normal acceleration due to gravity.
 * This happens in an Italian-made comic of The New Adventures Of He Man. A hallucinating boy jumps off the roof of his school, and Nocturna saves him by jumping off the roof after him. As he does that, he thinks: "I will reach him even though I jumped after him, because I am much heavier than him!" Nocturna then proceeds to grab the boy in mid-fall with one hand, grab a conveniently placed pole with the other hand and safely somersault to the ground.
 * In a Graphic Novel compilation of stories of "B-list" superheroes, there were four stories: one with Robin, one with Blue Devil, one with Geo-Force, and one with... someone that this troper has never heard of, before or since. Standard Charles Atlas Superpower here, no flight or mega strength or cool gadgets, he's just peak-fitness-plus-a-few. He was hunting an obvious Take That of the Nineties Anti-Hero formula, a vigilante with a shoulder-mounted smartgun that could give the Bat-computer a run for its money in facial recognition software. Unfortunately, one of his targets happened to have a twin brother.... When he mowed down the wrong brother by accident just as the "real" hero entered and got caught in the barrage trying to intervene, he jumped out of the window but was caught by mister wonderful. This trope is almost averted by the fact that the hero did a handstand on the windowsill and threw himself downwards; almost, because he had to get up from being shot (having flexed his pecs until the bullets popped out) and then run across the room to get to the window, coupled with the fact that the apartment was between 10 and 20 stories up at the most.

Video Games

 * One of the missions in No One Lives Forever portrays this trope straight, as it implies exactly running onto a Mook with a parachute and taking it from him in the air.
 * This is the same mission where a big Violent Glaswegian (in a kilt, of course) falls to the ground without a parachute and comes away without a scratch. All that consumed alcohol must have cushioned his fall.
 * Spy games seem to have a thing for this, as the James Bond game James Bond 007: Everything or Nothing features a level where Bond has to save the Love Interest from a death fall off of a cliff by jumping after her, catching up to her, and using his grapple hook to arrest their fall.
 * One of early boss fights in Metroid Prime 3 has Samus fighting Ridley....while falling down a very long elevator shaft. While portions of the fight has Samus standing on Ridley while the latter slows their descent with its claws, much of the fight has both opponents in a free-fall.
 * Isn't this an aversion? Since during the free-fall portions, Samus and Ridley are falling at the same speed... Someone who can either confirm or correct my memory get rid of this comment and edit the original example appropriately.
 * Ridley has, and uses, wings. That means both powered flight and controlled wind resistance. Terminal velocity doesn't really enter into it for him.
 * Averted in Final Fantasy VI, you fight while falling down a waterfall and several encounters worth of enemies keep popping up and sticking with you while you're falling (and fighting)
 * Battlefield: Bad Company 2 has you jumping out of a hole in the side of a crashing aircraft after two other people who are fighting over a parachute, shooting one of them and then taking the parachute.
 * Saints Row the Third: The mission 'I'm Free - Free Falling'.
 * Grand Theft Auto: The Ballad of Gay Tony has a mission where you throw a blogger out of a helicopter in flight, then you drop after him and catch him with your parachute.

Web Comics

 * In 8-Bit Theater, when the airship (deathtrap) the party travels in falls, it falls at two times the terminal velocity. "When I say deathtrap, I mean deathtrap."
 * Averted in Least I Could Do, which featured one Story Arc where the main cast went skydiving together. Rayne managed to fall out of the plane before hooking up his tandem harness with his instructor. The instructor managed to rescue him by falling to him and hooking them together - because the instructor put his arms and legs together and fell as straight down as possible while Rayne has his arms and legs spread out, so the instructor's air resistance was significantly lower. As well, since they were skydiving, it was a reasonable distance for him being able to catch up.
 * The characters in Dissidia Final Fantasy fall at different rates. Kuja can float lazily down from heights, but Kefka will drop like a rock. No falling damage, though.
 * In The Beast Legion, Xeus skydives into action to save Fyre from the shadow minions in this page.

Western Animation

 * Superhero shows have a lot of this. Superman and Batman spend a lot of time rescuing falling people/things, though Superman would actually be able to accomplish this by flying down (likewise, Terry of Batman Beyond had rocket boosters) at supersonic speeds. In one promo for The Adventures of Superman, a blatant Lampshade Hanging promised viewers that they'd "see Lois fall again".
 * Gargoyles had Goliath meeting Elisa by rescuing her from a fall off the top of Xanatos' skyscraper. Which he somehow manages to do despite her having a good 5 second head start. (The top level of Xanatos' skyscraper was actually above the cloud level—a necessary component of the spell to revive the titular Gargoyles—so it's possible Goliath had enough time to catch up to her.) A later incident has Matt Bluestone falling, but he spreads his limbs out as wide as he can to create as much drag as possible to allow Goliath to catch him in a pursuing dive.
 * IIRC, Elisa did have her arms and legs spread out, and Goliath dove head first after her. And Goliath bottomed out of their plunge only a few stories above ground level.
 * Cloud level can be pretty low, depending on what you count as "cloud" (compared to "fog".)
 * Macbeth later described the Eyrie Building as "the world's tallest building," and it was certainly taller than the other buildings in Manhattan.
 * The Perils of Penelope Pitstop, "Cross Country Double Cross": The Hooded Claw cuts Penelope's parachute and notes cynically that it's falling faster than she is.
 * Counter-example: Sherlock Holmes in the 22nd Century: "The Empty House": Sherlock realizes that Moriarty had staged his death when the two seemed to fall into an energy field. Watson had seen simultaneous impacts, which Holmes realized was impossible since they hadn't jumped at the same time.
 * Actually, both did fall at the same time, but Holmes managed to catch himself on a ledge and then threw a rock at the energy field. The fact that the impact on the field was simultaneous told him that Moriarty did the same thing.
 * Family Guy employs this with people, who tend to fall almost instantaneously while drunk or in some sort of humorous circumstance where a fall is imminent. Otherwise, physics is pretty normal.
 * Subverted on Futurama. The villain drops a precious gem from the top of a staircase, and Fry, who's up there with him, leaps to catch it; Leela shouts "No, Fry! You can't fall fast enough!" (Then Leela gets there in time to catch it by, ahem, running down the stairs... The commentary noting this was not really possible. Note that this episode involved the use of a cream that gave Leela and Fry superpowers, one of these powers being super speed.)
 * Speedsters would be launched into the air whenever they went over a hill or reached the top of a stairway, and even slight dips in the terrain would cause them to lose contact with the ground. Ergo, they have to have some sort of 'stick to the ground' force as a Required Secondary Power. If they can run over terrain that isn't 100% level faster than terminal velocity without problems, they can run downward faster than that too, and hence catch things falling out the windows of buildings. Of course, if it's a person, not a gem, they face other problems.
 * However, as with a car, if a speedster ran fast enough, with the right surface angling they could generate downforce strong enough to force them to the ground. (Air strikes them, and is deflected upwards, providing a downwards force on the speedster.)
 * Kim Possible jumped after Senor Senior Senior from a plane, and the slender cheerleader overtook this much bigger man. When they did Kung Fu. During the fall. Boo-yah.
 * "Nothing's impossible for a Possible."
 * Weight does not affect fall speed, it's all about wind resistance, and the slender Kim Possible would have a much smaller surface area than the not-so-slender Senor Senior Senior.
 * Happens frequently on Teen Titans when Robin has to catch something or save someone.
 * A common element of Cartoon Physics, but it usually works against the protagonist rather than in his/her favor. Falling objects reach the ground in whatever order will produce the most painful (for the protagonist) and funny (for the audience) result. Note, in these situations, almost everything falls faster than an anvil.
 * This editor's geology professor once joked that there is no constant acceleration of gravity in cartoons, only the initial acceleration to a constant speed—you can see this if you watch someone falling in a cartoon; the background flies past at the same speed the whole time. This, he said, is why Wile E. Coyote can fall off a cliff and walk away with only bruises.
 * Though normally everything falls faster than the anvil in cartoons for comic effect there is one exception. If the anvil is deployed from a backpack in place of a parachute it will suddenly notice that its an anvil and accelerate the attached protagonist groundward at breakneck speed.
 * Jackie Chan Adventures: In the first episode of season four, Jackie sneaks aboard the Dark Hand jet, only for the Enforces to simply strap themselves in and open the door in midair. A few seconds after he gets sucked out, Jade jumps after him with a parachute.

Real Life

 * Something like this actually happened on a skydive near Peterborough, England in the 1990s. A skydiver's chute failed and another more experienced skydiver actually managed to catch up with them, trigger their reserve chute and then his own chute a few seconds later. This troper recalls it as that the only thing wrong with the reserve chute was that the skydiver was too panicked.
 * Near the end of the Apollo 15 mission, one of the astronauts performed an experiment that involved dropping a heavy hammer and a feather (A falcon feather) from chest height on the surface of the moon. In the near perfect vacuum of the lunar surface both objects hit the ground simultaneously, leading the astronaut to comment that Galileo was right.
 * This is either Literature or Real Life, not sure, but there was a book years ago about how to survive a variety of odd situations, one of which was sharing a parachute. It's possible, but very, very, painful. Broken limbs abound because you have to secure yourself to the person with the parachute in a way you won't fall off when the chute deploys.
 * That's the Worst Case Scenario Survival Handbook, and you have to hook your arms through the front of their rigging and grasp your wrists, you dislocate both shoulders and possibly both people will break their legs too. But it's better than the alternative....
 * There's a stunt called "Mr. Bill" which entails doing this deliberately. It's done well before reaching terminal velocity though, and the other guy then jumps off and deploys his own parachute. Depending on the parachute I think it could be done at terminal with minimal injuries, my parachute (Spectre 150) has very soft openings. Landing two people with a chute designed for one is bound to be rough though - but still better than landing without one.