Understanding Movie Physics: Contact

Contact and the Implementation of the Twin Paradox

Are we alone in the universe? That is one of humanities biggest questions. In the movie, the writers tackle this topic in a fictional sense but try their best to keep it as realistic as possible. Such as the backfire from the religious community such a discovery might have and the physics that would go along with intergalactic travel (somewhat). 

During the course of the movie, and humanity discovers that they had been sent blueprints for a device that will send one human out into space to make contact with the aliens, the characters in the movie discuss what we call the "Twin Paradox".  The paradox is described like this:

Two twins exists. One goes on an interstellar/intergalactic trip at or close to the speed of light,        while the other stays on Earth. Hypothetically, when each twin decides to observe the other, they will notice that the other has experienced time dilation (time moves slower at higher speeds) and that their twin has aged to be older then them. However, this is impossible and that is where the "paradox" comes in, but there is an answer. Time dilation can only be properly observed from an inertial reference frame (a reference frame that is not moving or accelerating) therefore the twin that is accelerating off into space is not a valid reference point and that the twin on Earth is actually aging while the twin that is traveling is staying younger. 

Going forward, the problem in the movie is that they got this idea reversed. When the main character traveled through the wormhole which propelled her faster than the speed light, she experienced approximately 18 hours of space travel while on the Earth is happened so quick that no camera caught it causing people to believe she didn't travel at all. The main character should have experienced her trip on a shorter time interval than the time interval that occurred on Earth which is exactly what they discussed back towards the middle of the movie. The movie even contradicted itself! The movie should have had her return to an Earth where everyone was older or even dead. Just some kind of evidence that Earth experienced more time than she had.

Overall, the plot of this movie was good and while the ending left the audience somewhat unsatisfied I still believe it was a very enjoyable watch! But since the movie contradicted the Twin Paradox, an idea that they had explained in the movie itself, I am going to have the rate this movie a PGP-13.

Understanding Movie Physics Final Project: Captain America and Bucky's Helicopter (Captain America: Civil War)

Tug-of-War:

Captain America vs. Bucky and his Helicopter

Captain America: Civil War is an amazing movie that follows Cap on his journey to find and redeem his friend and stop a master mind from unleashing evil on the world, even if his own allies stand in his way. Ranging from topics such as psychological areas like brain washing to the realm of international politics, Civil War touches on many subjects that make a great movie. In our case, we will be studying the physics of the movie, specifically Cap's 'tug-of-war' scene with Bucky's helicopter.

In this scene, Cap is giving chase to Bucky as he is trying to escape. To make his getaway, the Winter Soldier jumps into a nearby helicopter and starts to take off; however, Cap is right behind him and jumps onto the leg of the helicopter, preventing it from escaping. Without anything to really keep him grounded, Cap is dragged to the edge of the building by the helicopter as Bucky is trying to get him off. Before being dragged all the way off, Captain America is able to grab onto a railing on the edge of the roof with one of his hands while still holding onto the helicopter and effectively stops Bucky from being able to escape, as he is able to hold back the massive force of the helicopter.

Just by looking at the scene, this action seems to be an amazing  feat for any man to accomplish, but just exactly how amazing of a feat is it? Let's see.

Our goal here is going to be to find the total amount of force Cap is applying to the helicopter to be able to hold it back. Posted below is a diagram of where each directional force is being applied in the scene: 

In the scene, we notice that the net force of the interaction is zero, as neither of the objects are moving or accelerating. This means that the net force of the interaction in both the x and y directions are zero as well. 

For the x-direction, this can be described as the force of Captain America (Fcx) and the thrust (Tx) cancelling each other out to equal zero (Fcx - Tx = 0), as they are both the same value (Fcx = Tx) but in opposite directions, which would indeed cancel out any movement in any x-direction as seen in the clip above. For the y-direction, it would be described as Cap's force(Fcy), the thrust of the helicopter (Ty), and the helicopter's weight (W), all cancelling each other out to equal zero (Fcy - Ty - W = 0).

In order to move ahead, we are going to have to estimate some values. For the thrust of the helicopter, we are going to assume that the helicopter has a weight of 12,000 lbs/5,443 kg which defines it as a "light helicopter" (a helicopter with a weight of 12,000 lbs or less), which possesses around 53,378 N of thrust power at the max weight. The helicopter in the movie seems to resemble many other types of light helicopters in size, so its safe to assume that it is has a similar weight and thrust values. Some trigonometry is also going to be used, so we are going to assume that, by looking at the scene, the helicopter is trying to move away from Cap at a 225 degree angle and the angle that Cap is pulling down on the helicopter is -45 degrees. 

In order to calculate the thrust in the x-direction, we must do some trig and multiply the total thrust by the cosine of the angle at which the helicopter is moving toward, that being 225 degrees, and we get a total of  -37,744 N. With the new Tx value, we can now actually find the total force of Captain America with a little shortcut thanks to the help of algebra. As stated before we know that Fcx = Tx and since we can figure out Fcx much the same as we did Tx by multiplying the total force of Captain America (Fc) by the cosine of the angle of which he is pulling down (-45 degrees) we can actually make a formula that solves for Fc by setting the Fcx and Tx equations equal to each other and isolating Fc. Worked out below: 

• After some calculations, we find that Cap is actually pulling on the helicopter with the exact same amount of force that the the helicopter itself is exerting! A total of 53,378 N which is equivalent to about 12,000 lbs of force! To put this into perspective, the highest world record of weight lifting was a total of 582 lbs lifted by a Russian man named Alexey Lochev. Cap topped this record by ALMOST 2000%! HOLY CRAP! Another way to look at it is that it takes about 4,000 N of force to break a human femur, and Cap applied about 13 times that amount in this scenario. It's amazing that he's not instantly killing every one his opponents that he fights with one punch. If it was in real life, then he certainly would be. Seems like Cap should be in the run for the title "Strongest Avenger," no?

Understanding Movie Physics: The Martian

A Discussion About The Martian and the Reality of Space

The Martian tells the story of an unfortunate man, portrayed by Matt Damon, who had been presumed dead and left stranded and alone on Mars. Through his own wit and ingenuity, he was able to survive long enough to make contact with NASA and make a plan for his return to Earth.  While Matt Damon's character faced one disaster after another over the course of the entire movie, he eventually made it home and now teaches a class about the dangers of space and how to survive it for young aspiring astronauts.

Compared to other science fiction movies, the space physics in  The Martian were relatively accurate by comparison. Referencing a list of Hollywood sci-fi space physics written by Philip Plait, we can make a good inference on how well The Martian stands as a model for good space physics.

1. Whoosh! Our Hero's Spaceship Comes Roaring Out...
• For the first of Plait's examples of proper space physics, he explains that one should not hear the "whooshing' or roar of a space engine in space as sound waves have nothing to travel on in the vacuum of space. Unfortunately, this is a rule that the movie breaks a lot. Look at the rescue scene for example, the audience is able to hear the quoted "whooshing" of the space crafts and the blowing of the oxygen coming out of Matt Damon's suit as he uses it to propel himself towards the Hermes.
2. ...of a dense asteroid field...
• According to Plait, the actual distance between asteroids in the asteroid belt is like a grain of sand divided up and spread up over hundreds of square meters. It would be very rare to actually come across an asteroid by this comparison! However, since there was an absence of asteroids in the movie, this rule cannot be applied to the movie.
3. ...banks hard to the left...
• Plait states that banking and turning sharply in space is quite unrealistic as there is no air in space for the such action to occur. In order to actually change direction, they need to enact some kind of propulsion such as a rocket firing in the opposite direction of where you want to go in order to actually maneuver in space. Examples of this in the movie is the crew increasing the speed of the Hermes as it entered Mars' orbit in order to be able to reach Matt Damon.
4. ...and dodges laser beams from the Dreaded Enemy...
• Plait states that you would not be able to see laser beams in space, but since laser beams were not a concept portrayed in The Martian then this rule need not be discussed.
5. ...who have come from a distant galaxy...
• In this section, Plait discusses the scale and sheer size of space in which the movie does a good of presenting this by discussing the lengths of the trip from Earth to Mars such as the scene where the Hermes crew members are discussing whether or not to go back to Mars for Mark, Matt Damon's character, and how many days it would add to their trip or any scene where the NASA members were discussing a trip to Mars as time and distance was major factor of their planning! As for enemies, this topic is irrelevant as no invading aliens were ever present.
6.  ...to steal all of Earth's precious water...
• Plait discusses reasons for an alien invasion, mainly the presence of water on Earth,  but again enemy aliens were not part of the movie so this rule can be ignored when analyzing The Martian. But Plait is not wrong when he states that there are other sources easier to access and harvest water from other than Earth.
7. The Dreaded Enemy tries to escape Earth's gravity, but is caught like a fly in amber
• Escaping Earth's gravity was never really concern in the movie, but Mars' gravity was an issue. Since Mars has a weaker gravitational pull than Earth it would be easier to break its gravitational pull. However, even though Mark needed to rocket himself off Mars in order to be rescued, he didn't need to escape its gravity. He only needed to be propelled far enough away from the planet so he could enter orbit, so technically this rule was not broken.
8. As stars flash by...
• Plait states in this section that space is so vast and stars are so far away that your movement or position in space would not effect how you perceived them. It also discusses warp speed and traveling at or faster than the speed of light and the concept that you see stars whiz by like the environment on Earth passing by as you drive a car in many sci-fi movies is false, but since such a form of space travel is not seen in the movie, this rule does not apply.
9. ...Our Hero gets a lock on them and fires! A huge ball of expanding light erupts past us, accompanied by an even faster expanding ring of material as the Dreaded Enemy's engines explode.
• There aren't any explosions in space portrayed in the movie, so this rule is irrelevant,
10. Yelling joyously, Our Hero flies across the disk of the full moos, with the Sun just beyond.
• In his final example, Plait discusses the inaccuracy of the phases of the Moon and that the Sun must be in between the Moon and Earth according to some sci-fi movies and how their phases are shown. This is rule is not broken since the Moon or any of its phases are seen in the movie.

In conclusion,  I would rate The Martian with a PGP. It presented most of the physics that applied to it pretty well, but there were some instance that it violated the rules of space physics that keep it from getting a higher rating.

Understanding Movie Physics: Fat Man and Little Boy

The topic of nuclear development and armament has always been a delicate and controversial topic. As seen in the movie, Fat Man and Little Boy, even the scientists who invented the bombs were divided over the ethics of such weapons before they were even finished.  The making of nuclear weapons provide a multiplicity of negatives that should sway anyone away from supporting their development.

One major thought that should come to mind when discussing nuclear weapons in the modern age is that of terrorism. Terrorism has been an ever present evil in the world ever since 9/11 and does not seem to dying anytime soon as each time its "defeated" another group just rises out of the ashes, as is the case with ISIS rising after the fall of Al Qaeda. Such groups are desperate to strike fear into their enemies such as the US and will do so with any means necessary. If such people were to get their hands on a nuclear weapon, whether they somehow developed the weapon themselves or stole an United States' or other foreign country's warhead, the resulting attack would be devastating. So, in retrospect, is it truly worth making and storing such dangerous weapons when there is even a slightest chance they can fall into the hands of terrorism?

Another topic is the wasted money that is poured into the United States nuclear arsenal program. Every year the US spends billions of dollars to work and develop the arsenal. To me that seems like a waste of money, attention, and effort that could be used in an area that could have a huge positive affect! All that money could be used for upgrading the US's education system, provide millions of meals to those suffering in poverty, and or fixing poor areas of American infrastructure instead of being wasted on a program that inspires nothing but fear and memories of conflict.

There are so many other topics that provide outstanding evidence against the use of nuclear development such as nuclear waste and environmental effects but honestly continuing on would be redundant and repetitive. Nuclear weapons, in my opinion at least, are so morally abhorrent that without a doubt their development should be banned and should be followed by mandatory disarming of all nuclear weapons.

Understanding Movie Physics: The Day After Tomorrow

Global warming is a topic of controversial debate in today's modern world. Some claim that it is a hoax, while others argue that it is a very real threat. While global warming is not as a immediate threat as it is portrayed in The Day After Tomorrow, it is still a very real threat that humanity has to deal with now before we leave Earth in a poor state for our the generations after us that they can heal.

The graph above, as researched and provided by climate researches working at NASA, show the level of carbon dioxide in Earth's atmosphere over thousands of years. It wasn't until around the 1950's , as seen above, that the level of carbon dioxide became dangerous.

In this video, NASA researchers have created a simulations that maps out the temperatures of the Earth since the late 1800s. It is important to note that temperatures around the globe are increasing both exponentially in both time and size as it gets closer to the present and that the last five years have projected the warmest global temperature in history, with 2018 being about 2 degrees higher than what the global average temperature had been in the 1950's. It is also important to note that the global temperature increase of the world only seemed to drastically increase around the 1940s/1950s which parallels the dramatic increase of carbon dioxide in the atmosphere.

Carbon dioxide is naturally in of itself a heat-conserving gas, and it is widely known that human development and innovation releases what we call greenhouse gases, carbon dioxide being a main one, into the atmosphere. With this information and the shared time frame in which both global temperatures and the presence of carbon dioxide in the atmosphere increase, it is reasonable for us to infer, just as many legitimate scientist have, that the increasing amount of carbon dioxide in the atmosphere produced from humanities factories, cars, cities, etc is what is causing rising global temperature as more and more heat is captured by the gas which signifies the presence of over all climate change and global warming.

Link below is the article from NASA's climate website from which the evidence used in this article:

https://climate.nasa.gov/evidence/

(In order to find the video on the website, scroll down till you see "Global Temperature Rise" and then click "More". The video will pull up right below.)

Understanding Movie Physics: Apollo 13

Apollo 13 and the Definition of Weightlessness

Weightlessness seems like it has a pretty straight-forward definition, but to be honest it isn't as simple as it sounds!

In many contemporary space faring movies, such as "2001: A Space Odyssey" or in our case "Apollo 13",  the characters seems to be experiencing "zero gravity" or "weightlessness".  It is a common held notion that out in the depths of space there is no force of gravity to act on the objects floating around out there, but scientists have figured out that such a thing is impossible. It is what keeps all asteroids and planetary bodies in orbit. The gravity of a star also has incredible reach as asteroids even beyond Pluto stay in orbit around the sun. It turns out that the force of gravity can get incredibly close to zero but never reach it and that the only way for there to be total zero gravity is to get infinitely faraway from any other object of mass. 

This is where the idea of weight comes in.  The weight of an object is dependent on that object's mass and its relationship with the gravity of the planetary body that object is on or around. However what humans perceive as weight is actually a force that we call, a normal force of an object. The normal force is a force that resists the force of gravity as it is an "opposite reaction" to the initial action that is gravity, meaning that it has the same amount of force but an opposite direction and its this resistance that we perceive as weight. And the lack of this normal force is what helps define weightlessness.

The normal force of an object can only be removed if an object is sufficiently removed from a planetary that it is considered to be in free fall. Free fall is defined as a situation where the only force acting on an object is gravity. An example of this are astronauts on the ISS (which actually experiencing a very long or extended free fall but is going at fast enough speed so that it doesn't plummet to the Earth)) or for a film example is any scene in 'Apollo 13" where they are floating in their spaceship between the Earth and the Moon where the gravity is weak but strong enough to still affect them.

Therefore, in order to conclude or summarize, the only way to experience "weightlessness" is to remove the normal force of an object by putting it in free fall so the only force acting on it is gravity and that the object is at a sufficient distance away from a planetary body so that its gravitational pull is relatively small and is going at a fast enough speed to keep it from falling.

I rate "Apollo 13" a PGP level movie.

Understanding Movie Physics: Avengers: Infinity War

Avengers: Infinity War. The beginning of the end of Marvel's Infinity Saga. It is an amazing movie that immortalizes some of Stan Lee's famous comic book characters. Filled with action packed fight scenes between humanities greatest heroes and aliens, such as Thanos and his Black Order,  who seek destroy half of all life in the universe, Infinity War tests many forms of physics, but in this blog we are specifically going to look at scenes that defy Newton's Laws of Motion.

Scene 1: Doctor Strange and Levitation

One of the simpler defiances lies in the power of levitation or unaided flight. Many characters like Iron Man or Star Lord have rocket propelled forms of flight, meaning there is a force keeping aloft, however, for characters like Doctor Strange, they have no force keeping them in the air. According to Newton's Second Law, gravity acting on a living being with mass (which Doctor Strange definitely has)  while in the air means he should be falling downwards. Since Doctor Strange does not
have a downward facing force to keep him in the air, he should be falling to the ground but since that is not portrayed in the movie, this counts as a violation.

Scene 2: When He Should Have Gone For The Head.....

In this scene, Thanos has just killed Vision and inserted the Mind Stone into the Infinity Gauntlet. In an attempt to prevent the Snap, Thor flings Stormbreaker into Thanos' chest but fails to kill him. It instead gravely wounded him, but not enough to prevent Thanos from killing off half of all life in the universe.

The problem with this scence is that when Thor hit Thanos with Stormbreaker, it should have created a crater or indent in the earth of some sort but it didn't. This violates Newton's Third Law of Motion. The downward force created by Stormbreaker is enough to create a crater as evidenced by a previous scene where Thor slams down is hammer and creates one. The same thing should have happened with Thanos. The force from the impact would cause an opposite upward reaction from the ground around the impact point which leads to the formation of the crater. Even though in this scene Stormbreaker hit Thanos and not the ground, the force would have channeled through him and still have the same effect.

Scene 3: The Hulk in the Hulk Buster

https://www.youtube.com/watch?v=1tyHcCwkT0Y  

(Sorry this one is a link! It was the only way to get this scene in!)

In this scene, Bruce Banner has been equipped with the Hulk Buster armor, a huge metal suit designed to defeat the Hulk in violent confrontation. He is running across a grassy field towards the front lines of the battle that is about to commence. But again, the physics in this scene is screwed. Much like the previous scene, this one is a violation of Newton's Third Law. It is violated by the non-existence of an impact craters. The Hulk Buster armor is a giant heavy metal contraption that is exerting a good amount of force on the ground beneath him as he his running, but no crater (aka the opposite reaction) is created which in fact should be present.

Understanding Movie Physics: Armageddon

Armageddon. The end of the world. Humanity's execution by meteor. That is what would have happened in the movie if Bruce Willis' character, Harry Stamper, and his team had not drilled a hole in the meteor, threw a nuke inside it, and blew it up. To be brutally honest however, that plan would have ultimately failed and humanity would have perished...even NASA has confirmed that the nuke idea used in movie would fail. Luckily enough, in reality, NASA has contingency plans in place that actually will protect the Earth from asteroids. 

Last year, the White House Office of Science and Technology released a plan called the "National Near-Earth Object Preparedness Strategy and Action Plan". The document describes 5 goals NASA is going to take over the next decade to deal with any asteroid threat. None of which requiring a drilling team - or even an a regular astronaut for that matter- to go into space and forgo the threat.

It will be to much to go into the specifics of the specifics of the objectives that are laid out in the 18 paged plan, but it will be good to provide a basic overview:

• Objective 1: Improve Surveying Methods and Technology 
• In a sense, find areas to improve existing survey telescopes and provide those using them with new training to make them proficient in the use of the new technology in order to upgrade NASA's process of detecting, tracking, and analyzing asteroids that may pose a threat to the Earth. These improvements will help "reduce current levels of uncertainty and aid in more accurate modeling and more effective decision-making," as described by the document.

• Objective 2: Estimation of Probability Improvement
• After improving the tracking and basic analyzing of an asteroids, NASA wants to work on upgrading the process of putting all that information together to get the most accurate prediction possible of when and where on the Earth a possible asteroid could impact the Earth. With this information, more "emergency-handling" qualified agencies like the Federal Emergency Management Agency (FEMA) can come up with the best way to approach the situation when dealing with an incoming asteroid.

• Objective 3: Deflection Ideas


• Once as much possible information and estimations have been made, NASA is tasked inventing new technologies and methods that will help remove the threat of an incoming asteroid, primarily by moving it out of the way. One such method is the idea of a Near-Earth Reconnaissance mission in which a satellite or spacecraft would move in the direction of the oncoming object and in some way move it out of line with the Earth and neutralize the threat (this is where the new technologies I mentioned before will be needed).
• NASA plans on testing its Double Asteroid Redirection Test (DART) in 2022 when it encounters the asteroid Didymos in 2022. The plan for this is to launch the DART probe in 2021 and by some time 2022 have the probe crash in the asteroid at 21,600 mph and study the effects and determine how much force is needed to move an asteroid that could potentially hit Earth out of its orbit.

                                            

• Objective  4: Improve International Teamwork
• This goal aims to reach a high enough global cooperation under the guidance of the United States in order to properly prepare the rest of the world of an asteroid strike and the aftermath of one should deflection attempts fail.
• To help achieve this goal, NASA's Planetary Defense Coordination Office is constantly in talks with the United Nations in order to decide what a global response to an asteroid strike should look like. 

• Objective 5: The Job of the United States
• The final objective tasks the US government and all its appropriate agencies with developing a plan in the event of an actual, potentially devastating asteroid threat and a plan for a possible aftermath as well.
• NASA's job would mainly be enacting NEO impact plans in hopes of deflecting the asteroid and FEMA would work to notify anyone who would be threatened by the asteroid and would send out emergency responders to help with a recovery process if its needed.

Understanding Movie Physics: Eraser

Arnold Schwarzenegger. Action scenes. Rail guns. Inaccurate physics. All of these factors contribute to the thrill that is the movie Eraser. However, it's that last factor, inaccurate physics, that tends to bug many of this movie's viewers. Especially the physics that violate the law of the conservation of momentum.

The scene posted below, like many of the other's seen throughout of the movie, show a human, often either Arnold's character or one of the enemy thugs, firing a weapon called a rail gun. In the movie, a rail gun is explained to be a gun that uses electromagnetic energy to fire a lightweight aluminum bullet at almost the speed of light, and it is here that we discover the inaccuracy of these scenes.

Eraser Scene:

https://youtu.be/IDC-tIQpJ_0 

Whenever one of the speeding rounds hits a human body, that individual is most often sent flying across whatever environment they are in , but the shooter is always left unaffected and in the same position as they were before. This is the violation of the law of  conservation of moment as previously mentioned, which states "In the absence of external forces interacting upon an object or a system of objects, the total momentum will not change". This basically states that the momentum before and after the collision must be the same. Therefore the shooter must face a negative recoil velocity that sends them flying backwards that is equivalent to the positive velocity of the bullet being shot forward in order for the momentum's of each object to cancel each other out and get a total momentum value of zero that was present before the collision. Another approach is that neither the shooter or the one shot face any kind of momentum that would send them flying and instead don't get sent flying like before.

Due to the complete disregard of the law of conservation of momentum, I am rating this movie with an RP (retch physics) rating.

Understanding Movie Physics: Mission Impossible 3

by Anthony Forcella

Mission Impossible III seems to be the focus of many when it comes to those who crave action scenes with guns and explosions, chase scenes through maze-like cities, and stunts that seem impossible to the average man. While many of these scenes are appealing to the eye, the physics behind them are questionable. At some points the film tries to apply math and physics to some of the stunts presented, but for us, the ones in search of the truth, are not satisfied with those explanations and will analyze them ourselves to test the actual possibilities.

Scene 1: The Building Swing in Shanghai

This scene is perhaps the most famous (or infamous to movie physics critics) of the action stunts portrayed in the movie. Prior to the actual scene, Tom Cruise's character, Ethan Hunt, proposes the idea to swing from a point on a neighboring that is higher than the one he has to break into and makes some measurements in order to try and validate the physics behind the idea. So, as our job as movie physics analysts, we test the actual reliability of these measurement and the scene of the jump itself, and to do that a question about it must be formed. The most obvious of which being:

Can Hunt actually make the full distance of the swing?

Referenced from the planning scene from the movie, the taller building (Point A) is measured to be 226 meters high and the smaller (Point B) to be 162 meters in height. The distance between Points A and B was measured to be 47.55 meters. He starts off with a sprint which we can estimate to be about 9 m/s (Initial velocity) before he jumps off the edge of the first building. It takes him about 25 seconds to complete the stunt before separating himself from the jump cord and since the jump is occurring in mid-air we have to calculate how fast gravity is pulling him down and decelerating him which we can assume is -9.8 m/s^2.

Scene 2: The Leap at the Bridge Battle

In this scene, Hunt has just been attacked by a group of enemy forces and speeding drone. The attack results in major damages to the bridge they are on and the loss of their captured enemy, Solomon Lane. In an attempt to recapture Solomon, Hunt gives chase to the enemy on foot and eventually finds himself cut off from them with the edge of the bridge being on his left, and giant pile of rubble to his right, and a gaping hole out in front of him. In order to get to Solomon, he leaps across the gap and barely manages to make it across. The question here to ask is: 

Can Hunt make the leap across the gap?

To begin with, we are going to need to estimate the speed at which Hunt is running to be about 9 m/s and he seems to be pushing himself off at an angle of 45 degrees. We also need to determine the length of the gap (distance Hunt needs to travel) in order to determine if the velocity of Hunt and the angle of his jump is sufficient enough to cross the gap. By analyzing the leap itself, we can see that the gap measures about 5 leg-lengths across. Since we cannot determine the actual length of Tom Cruise's leg, we have to use the average length of a human leg which is about 75 cm which we go on to multiply by 5 to get a total length/distance that Hunt has to jump being 375 cm or 3.75 meters. We also need to calculate the total amount of time that Hunt takes to cross the gap which we can assume by watching the scene and considering the effect of slow motion that it takes Hunt about 2 seconds to cross the gap.  And again we also need to include the effect of deceleration that gravity has on Hunt which we can assume is -9.8m/s^2.

Scene 3: Repelling at the Vatican

In an attempt to capture Solomon Lane, Ethan Hunt has to sneak his way into the Vatican. Amidst his variety of costumes and false personas is a scene where Hunt repels down from a wall and suddenly stops inches from the ground. The question we will ask here is:

At what velocity did Hunt repel down the wall?

Before he begins to repel down, he measures the total height from his position on top of the wall  to the ground to be 16.55 meters with a small electronic device. Hunt goes on to fall off the edge without any initial velocity (Vi) so we can assume that it can measured as 0 m/s, and the same can be said of his final velocity as he comes to a complete stop (Vf = 0 m/s). Since Hunt is letting gravity control the acceleration and not having any other outside force propel him we can use the acceleration due to gravity on Earth (9.8 m/s^2 ) as his acceleration. Once Hunt comes to a stop, he reaches down to the ground to steady himself. The average length of a human are is about 0.635 meters, but given that his arms are bent at about half lenght we are going to assume that he is about 0.3175 m off the group at the time of his complete stop.