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Variable Terminal Velocity

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"Bulma, how high would you have to fall from to hit 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/second-squared)note  that the rest of us have to deal with.note 

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.

This is possible when you factor wind resistance into the equation (for example, if you were to drop something very light with a large surface area and then threw something small and dense after it). 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 that effect to be workable in your favor. Someone falling head-down has a terminal velocity about 1.5x faster than someone falling belly-down (180mph vs. 120mph). A professional in streamlined clothing and gear can hit about 2.5x the belly-down speed (about 300mph).

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.

See also Catch a Falling Star, Not the Fall That Kills You…, Soft Water, Stairs Are Faster.


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    Anime and Manga 
  • A similar situation occurs in My-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+, 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.
  • 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.
  • 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 Children 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. Justified since Sephiroth has enough Super-Strength to "lift" Cloud. A better example occurs earlier, when Rufus and Kadaj are on the top of a building.Rufus reveals that he had Jenova's head all along, and proceeds to throw the box containing it off the building. Kadaj tries to hit him with magic, but he dodges by jumping off the building . Kadaj jumps several moments after him and still manages to fall fast enough to go past Rufus and grab the box before hitting the ground. Somewhat justified by the fact that the building explodes about a second after Kadaj jumps, meaning the shockwave from the explosion could have conceivably accelerated him past Shinra.
  • 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 ˝'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.
  • When Tsukiyo (magically doll sized) falls off a building in The World God Only Knows, Keima immediately jumps off to save her. After catching up to her, they then have enough time for a romantic mid air kiss before Elsie saves them.
  • In Patema Inverted, the heroes Patima and Age falls more than they moves normally. So we have many occasions to the following behaviour: After some strange physical experiments the "inverted" and the people of Aiga are affected by opposed gravity. And when Patima and Age holding each other, they weight effective their difference. But this doesn't explain, why they fall with constant speed on the one hand but can jump ballistic on the other hand.

    Comic Books 
  • 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 with Robin, Blue Devil, Geo-Force, and one other. 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 '90s 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.
  • During Secret Wars II, the Beyonder, in the body of an ordinary human, blithely walks off the roof of the Heroes for Hire building. Luke Cage leaps off to catch him, reasoning that since he's heavier, he'll fall faster. He's unable to confirm this theory, as the Beyonder simply teleports away, leaving Luke to crash to the pavement alone.

    Films — Animated 
  • Happy Heroes: The Movie: Both times Happy S. has to dive after Careful S. to save him, he is able to fall fast enough to be able to catch up with him. Perhaps justified in that Happy S. gets an extra boost through his power, however.
  • Averted in The Incredibles when Elastigirl and her kids drop out of the airplane. All three fall at the same rate.

    Films — Live-Action 
  • 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. In other words, A Wizard Did It.
  • James Bond
    • In the opening sequence of GoldenEye, 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 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 comedy 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.
  • 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.
  • Done realistically in Star Trek (2009). Sulu falls off the Romulan drill with no chute, and Kirk jumps later and catches him. However, Sulu only has five seconds on Kirk, Kirk catches up by exploiting air resistance as he profiles his body and Sulu spreads himself out, and they're VERY high up (they fall for more than a minute all told). Of course, it's all for naught as Kirk's chute breaks immediately and they have to rely on a miracle beam-up by Chekov on the Enterprise.

  • As their ability to fly fails in So Long, and Thanks for All the Fish, 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.
  • 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.
  • The Feruchemical power to store weight has an interesting relationship with this trope. While this probably isn't how the power actually works, the physics play out roughly as if the Feruchemist is changing his density. So in Mistborn: The Original Trilogy a Feruchemist can jump off a cliff, store most of his weight, and air resistance will slow him to a manageable speed, as if his body were made of Styrofoam. On the other hand, when Waxillium Ladrian taps a bunch of his weight while jumping, he doesn't fall much faster (air resistance was presumably negligible even with his natural weight), he just falls a lot harder.

    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 has 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!) Then, after Ace steals the parachute, floats to the ground, rescues the local princess, takes off on a flying motorcycle, and skywrites "Smoke Me A Kipper, I'll Be Back For Breakfast", two guards who have witnessed all 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.
  • Power Rangers Lightspeed Rescue has Ryan catch Captain Mitchell this way. They try to justify it by showing him pushing off the cliff in a manner that would launch him faster, but that would only make sense if he did it virtually instantaneously, rather than a second or two later. The implication of the scene is still that he's accelerating much faster.
  • Parodied here, along with several other things.
  • A very specific version of this trope was proved true by the MythBusters. It is in fact possible for Skydiver A (In vertical "bullet" posture) to overtake Skydiver B (who is in "spread-eagle" posture and has a head start) due to the difference in wind resistance.

    Theme Parks 
  • The idea behind 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 much scarier: the elevator car has cables to pull it up, but also cables on the bottom that pull it downwards even faster than the normal acceleration it would experience in free-fall. Appropriately enough, many agree that this is one of Disney World's most intense thrill rides.

    Video Games 
  • In No One Lives Forever, one of the missions portrays this trope straight, as it implies exactly running onto a mook with a parachute and taking it from him in the air.
  • James Bond game 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 belt-grapple hook to arrest their fall. Considering he manages to come to a near immediate stop without breaking in half and falls for a good 60 seconds, they probably weren't going for realism.
  • Averted in of early boss fights in Metroid Prime 3. Samus is fighting Ridley....while falling down a very long generator shaft. Ridley uses his wings and claws to speed up or slow down respectively, but outside of that both characters are falling at the same speed.
  • 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'. You catch up to a parachute-less Shaundi, catch her, then DROP her, go through the plane again, and RE-catch her. Shaundi is less than happy.
  • Grand Theft Auto IV: 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.
  • Most of the characters in the Super Smash Bros. series have a variable terminal velocity and reach it almost instantly. Starting from Melee, these differences became more pronounced, especially the case of Fox, who for some odd reason falls twice as fast as most of the cast, which works both for and against him. A character's maximum falling speed also increases significantly if you're using a Metal Box.
  • Sonic Generations contains several sections whereby you fall down a vertical shaft dodging obstacles. Pressing the boost button here makes Sonic fall faster. This is essential in the sixth boss, where you not only have to dodge obstacles, but actually have to catch up with the boss itself while falling. It's not falling, it's fleeing via rocket propulsion. You still catch it. Its somewhat justified in that Sonic eagle-spreads his limbs or streamlines himself to alter his wind resistance. Supplemental material also reveals that while he can't use his quills to glide like Knuckles, he can also use them to slow his fall.
  • 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.
  • Borderlands 2, along with the other games in its franchise, features an interesting version of this: supposedly, the gravity on both Pandora (where the first and second games take place) and Elpis (where the Pre-Sequel takes place) is low enough that terminal velocity is low enough that characters will take no damage from falling whatsoever. This, however, only applies to the areas in the game where you're supposed to go: step off of the map, and you'll find yourself falling to your death from a distance that you should be able to drop down with no trouble whatsoever.
  • Super Mario RPG: When you fight Bowser at the beginning of the game, he is on a chandelier being held by a Kinklink, and opposite him is another chandelier likewise held by a Kinklink, Mario standing on it. When Bowser's chandelier drops, it is followed shortly by Mario's, but it's able to catch up with his.

    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.
  • Justified in Narbonic:
Artie: "I estimated a minute change that with a greater starting velocity I might catch up with Helen before we both hit freefall. Admittedly it may have been prudent to have figured out what to do next oh well aaaaagh"

    Web Original 
  • Happens in Red vs. Blue, after the Director blows up the skyscraper in season 9. Tex kicks the Sarcophagus off the roof, then the others jump after it and end up catching up to it. However, it's done fairly realistically—the Sarcophagus isn't exactly streamlined while the Freelancers chasing it have their limbs tucked in until they reach it, at which point they spread out to more like the "boxman" position to match its speed. York and Carolina getting "caught" by Maine in the Warthog is probably an example of this, though.

    Western Animation 
  • 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 five-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.
  • 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.
  • Defied in the Sherlock Holmes in the 22nd Century episode "The Empty House": Sherlock realizes that Moriarty had staged his death when the two seemed to fall into an energy field. 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.)
  • Happens frequently on Teen Titans when Robin has to catch something or save someone.
  • 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.
  • In Star Wars: The Clone Wars during the Zygerian-arc Ahsoka saved a Togruta slavegirl who fall from the holding cell's Trap Door, by jumping after her, arriving ontop of the rescue ship before her, and catching her. Might be justified, as she probably used the Force to first speed herself up, then to protect themselves from landing too hard.
  • In one episode, Darkwing Duck finds himself falling with a coconut-shaped bomb next to him, having involuntarily been ejected from his plane. He tries to throw it up and away, and it catches up. Twice, same result. When he isn't throwing it, it doesn't pass him either. Yet more ridiculously, when he throws it to the side, it returns; he just resigns himself to fate at that point.
  • Discussed in an episode of The Secret Saturdays. Drew's brother relates a story from his adventures that involves him leaping out of a plane to catch up to someone who'd jumped before him. Doc skeptically asks how he managed to do so after reaching terminal velocity. The answer? "I'll show you terminal velocity."
  • This is a stock trope in the Wile E. Coyote and the Road Runner cartoons. If the Coyote ends up going off a cliff at about the same time as a boulder, anvil, or other heavy object, he will hit the ground first, and then the other object will land on him.

  • Played straight on skydiving. Some people actually do fall faster than the others - the terminal velocity is actually dependent on the body mass/body surface ratio, as the drag coefficient is dependent of the surface area. They are known as "fast descenders" When doing formation skydiving, other skydivers may need to take on lead weights to keep on with their free fall velocity.
  • Likewise, a skydiver can change his or her free fall speed by altering his/her surface area. When you pull your legs up or increase the body bend, you will fall faster, and when you bend your legs downwards, you will fall slower. It is also possible to move forward and backward while in free fall, and also bank.
  • 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.
    • Confirmed by the MythBusters when they took on the movie Point Break (1991) (one scene, three myths).
      • Though 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.
    • The "boxman" position is known also as stable position. It is indeed stable - the center of gravity is low so the skydiver will not tumble or roll in that position. This is critical for deploying the chute so that it will not get tangled.
    • This actually happened in the case of a particular skydiving incident - the first man struck his head while diving out and was rendered incapable of operating his parachute, so his companion jumped after him, caught up, and activated his parachute. This is explained because the first man was tumbling and providing significant air resistance, as explained above.

    Real Life 
  • The terminal velocity is actually dependent of not only the gravitational acceleration, but also drag. Mathematically the terminal velocity is expressed as v = sqrt(2mg/ρAC) where m = mass, g = gravitational acceleration, ρ = air density, A = area of the free falling body and C = drag coefficient. The terminal velocity of a human being on free fall in stable spread eagle position is 54 m/s (180 ft/s). A skydiver will attain that in twelve seconds.
    • It is perfectly possible for a skydiver to attain higher velocities by reducing one's area, such as in delta position or vertical dive. Performing the changes of speed and direction are actually part of the skydiving training program.
  • 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. The only thing wrong with the reserve chute was that the skydiver was too panicked.
  • Near the end of the Apollo 15 mission, astronaut David Scott 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 Scott to comment that Galileo was right.
    Scott: [cheerfully] How 'bout that?