Sunday, November 29, 2015

Mind/space/time-bending physics

Time and gravity are related in very interesting ways. Before learning about them, and doing research into it, it never occurred to me that they might be very fundamentally connected.

Objects with mass in the universe create warping of spacetime. In these warped regions, time runs slower, especially as you get closer to the center of the mass responsible. Other objects of mass tend towards these areas of slower time. The higher the mass, and therefore the greater the warping of time, the more intensely those objects are attracted to that area. This effect is known as gravity. In black holes, where spacetime is incredibly warped, objects are pulled violently in. Around the Sun the effect is not as extreme and so the pull that its mass creates is balanced by the centrifugal force of the planets orbits, keeping them carefully spinning around.

To give an idea of how incredibly dense black holes are, the .7in circle represents the size of the Earth if it were to collapse into a black hole today, retaining it's original mass.
Black holes are extremely dense, because they continuously pull in matter and compact it into infinity. Because of this density, time is warped large amounts as you approach the center of it. At its event horizon, time stops and gravity is so intense because of this that nothing can escape past that point, not even light. In Interstellar, this is why it cost them so much time to land on Millers planet. As the closest orbiting planet to the black hole, time slows down to seven years for every hour spent on its surface.

This time distortion can be measured even on a much smaller and more local scale. An atomic clock was sent up to 10,000km on a rocket, and radio signals were used to compare it to a clock kept on the ground. It was found that time flows by about 30 microseconds slower on the ground than at that altitude.

Because of the time difference between Earth's surface and its atmosphere, orbiting satellites must compensate in order to send accurate data. At 20,000 feet, time runs faster by 40 microseconds per day. For GPS triangulation to work, where signals are bounced off three or more satellites and the transmission time is carefully recorded to pinpoint your location, the satellites must convert the reading to "surface time".

Additionally, radio signals were sent to the Voyager missions as they orbited Mars. There was a discrepancy here as well. It took more time than expected for the signals to bounce back when they crossed closer to the Sun. Because radio waves travel at a constant speed, the only explanation is that the amount of space that they had to cross was a longer distance than what traditional methods would predict. Signals that passed closer to the sun were warped more than signals traveling farther from it.

This is also related to a phenomenon called gravitational lensing, where large masses cause light to bend around them. This allows us to see distant celestial objects that would otherwise be too dim or obscured by other bodies in our line of sight. It also sometimes causes multiple images of the same object to appear, at different points in time because of the difference in the distances the light traveled. In the case of Einstein's Cross, four distinct images of a distant quasar can be seen. Because of the time difference, when it went supernova scientists were able to watch it unfold four times over, over a period of several days,
 Hubble Space Telescope image showing the quadruple-lensed supernova

Because of the discovery of phenomena like this, we've come a long way in understanding what we're seeing when we look into the night sky, and how different forces in the universe affect each other. 

Saturday, November 21, 2015

Star Trek: sending things places really fast

The biggest issue in the plausibility of science fiction set in space is just the sheer distance that is being dealt with. Often, because it is such an obstacle to the plot, physics, in particularly relativity, are quietly cast aside. However, some creators attempt to tackle it in a way so that instead of directly violating known principles, they simply expand on currently theoretical concepts.

To support the rapid-action pace of Star Trek, a way to get from location A to location B in a timely manner is very necessary. If the crew of the Enterprise receives an emergency signal, they need to reach their target destination before the ship that sent the signal is long gone and whatever enemy that was threatening them is an extinct race. The series is set in the Milky Way, which is about 100,000 light years across. Traveling even a fraction of that distance at the speed of light would still see thousands of years passing from an outside perspective. The writers needed a way to get around this potentially huge plot hole while still maintaining a vague adherence to the laws of physics. Since they knew from the theory of special relativity that it's not possible to travel faster than the speed of light, they developed an alternative. Instead of the ship moving through space at an impossible speed, the ship pulls and bends space around it to reach its destination. This way, they can avoid the restrictions imposed by relativity. Relativity only applies to objects moving through space, not space itself. A theoretical "warp drive" would be able to contract spacetime in the direction of desired travel, while expanding it in the opposite direction. The ship, remaining stationary, can "warp" great quantities of spacetime around it to effectively "travel" immense distances fairly quickly.

The writers developed a system of "warp factors" to quantify this in terms of the speed of light:

Warp FactorNumber of times the speed of light

Even while using this highly theoretical method of travel, they imagined a limit for it, described as the impossible "Warp 10".

Is it possible outside of science fiction? NASA thinks maybe, eventually. Many scientists have done extensive research into it, as it would mean distances that were previously scientifically of the question could become possible. One such theoretical real-world equivalent that has been explored is the Alcubierre drive. Conceptually nearly identical to a warp drive, it has been proven to be mathematically sound, though that doesn't guarantee physical possibility. Initially, the calculation for it involved more energy than present in the observable universe, but has since been scaled down to about the energy equivalent of three solar masses, or around 3144 times the mass of Jupiter. 

A second technology that is necessary for the Star Trek universe to form a cohesive storyline is an ansible. When traveling distances of the scale allowed by warp drive, communication becomes an issue. Radio waves, which travel at merely the speed of light, would take the equivalent light years between ships or planets to be received. A distress signal could take tens or hundreds of years to reach its intended receiver even at many times the speed of light. This is circumvented by sub-space communication, with a device typically given the general name "ansible" in science fiction. An ansible could theoretically work by two methods. The first is by the creation of a "micro-wormhole", or a tiny shortcut through spacetime. Signals sent through this could reach their target in a fairly timely manner, depending on the location of the wormhole. The second option is through the phenomenon of quantum entanglement, where a pair of particles are "entangled" in such a way that a change in the state or orientation of one particle will affect the other, regardless of space or time. Measurements of the properties of entangled particles have found that they are appropriately correlated. For example, if one is spinning clockwise, the other will spin counterclockwise. Manipulating the spin of one would affect the spin of its counterpart, The particular usefulness of this is that messages could possibly be sent this way through a kind of binary system. At a delay of a hundredth of a percent of the speed of light, communication would be near-instantaneous. It has been argued that this would affect causality, and therefore would not be possible in practice, however predictions of the connection between entangled particles have been experimentally proven. It seems that the largest issue would be in developing meaningful communication through this method.

Sunday, November 8, 2015

Creation/Destruction of a Monster

Watching Fat Man Little Boy and Gojira back to back was an interesting experience, in the extreme contrast of both the style and moral positions. 

In Fat Man Little Boy, many of the scientists had the viewpoint that they were just doing their jobs, and were not responsible for any outcomes of the weapon that they create. This has a similar ring to it as the Nazi general's defenses during the Nuremberg Trials, that they were "only following orders", and therefore not responsible for the crimes they carried out. The scientists said that they simply carried out their assigned task, and what happened with the result was beyond their control.

Contrary, the scientist in Gojira took full responsibility for the weapon he created. He could have used a similar excuse, that he just discovered the method for developing the device, and was not liable for any uses it may be put to. Instead, he accepted ultimate responsibility and destroyed all knowledge of his research, including himself, so it could never be duplicated and used for more sinister things after taking down the monster. Unlike the american scientists, who could disassociate themselves from blame in their minds, he felt fully accountable for anything that it might be used for, even when out of his hands. 

However, if I were in the position of the american scientists, I feel as though it might not be quite as clear-cut as it seems from a broader outside view, like many things. By putting it on the executives who have the final decision of what application your research will have, you can easily personally relieve yourself of blame. The scientists probably realized at some level that what they were doing went against their morality, but rather than struggle with cognitive dissonance, they rationalized it to themselves so they wouldn't feel guilty. I can see how it would be exciting to be involved in something so monumental. In Fat Man Little Boy their awe at the massive mushroom cloud produced from the first major test demonstrates this; they were so caught up in the project that even seeing its power and destructive capability they were thrilled instead of horrified.

I can find other ways to rationalize it as well--if you turned down the opportunity because you were morally opposed to it, someone else would easily fill your place, and nothing would be different. Scientists, like many holders of technical jobs, are fairly replaceable. Someone will step up to the job, if not you, the next guy. And if it's going to happen regardless, it's almost like a cop-out to let someone else take your place just so you don't have to feel guilty. What if you could do a better job, make it safer?

It's scary that it is easy to think like this, because you are absolutely responsible for how your research is utilized. To not thoroughly consider the possible drawbacks and impacts is just careless. Unfortunately, many destructive things have been created by well meaning people. However, intent still doesn't factor into the outcome. And especially for the Manhattan Project, the scientists knew full well what they were developing and what it would be used for.

If I were a scientist and asked to take part in research that had weapons applications, I would like to say that I would absolutely decline. It isn't something that I could ever feel comfortable or good about doing. If it was my only career option, I would rather choose something that felt like I was affecting the world in a positive way to offset the people who chose the other path. 

Sunday, November 1, 2015

Global Climate Change: Yep We're Doomed

Global warming is an unnecessarily controversial issue. Many people look for any reason they can to deny it, on a range from accepting the data but believing it to be a natural part of the Earth's "temperature cycle", to outright choosing to think that the high ratio of scientists who support that humans are causing global climate change (97% is the figure popularly circulated) are somehow all in it together to create a giant conspiracy.

The most rational argument I've commonly heard is the one acknowledging that global warming is occurring, but it's not a "big issue" because it's a natural process. As my art history professor so eloquently said:

"Sure the Earth is warming a little. But, you are arrogant to think that humans could cause this. It is just a part of the natural cycle".
First - even if it was just a natural process, that doesn't automatically disqualify it as an issue of importance to humankind. However, data collected from ice and tree cores, as well as ongoing monitoring of aspects such as temperature, snowfall, rainfall, ocean surface temperature and deep sea currents, help put together a timeline of the earth's climate history.

What we can determine is that though there have been many periods of extreme temperature in earth's past--from ice ages to times when much of the planet existed as a tropical climate, there were always legitimate outside factors that contributed. The biggest of these is the effect of the Sun. The Earth's orbit goes through regular calculable changes which affect how long it is close to the sun, as well as what areas of the Earth are more exposed to it's heating effects. About every 100,000 years the Earth cycles through an elliptical eccentricity of orbit. The more elliptical the Earth's orbit, the more time it spends away from the Sun. Cycles such as these plunge the Earth into predictable temperature swings. There is no such thing as a "natural cycle" of temperature variation, there must be an external factor that's "forcing" the shift. At the moment, none of the historical factors line up. The Earth is not just happening to warm up--we are causing it.

Milankovitch Cycles Eccentricity, Obliquity Tilt, Precession w/caption

In just the last century or so....

However, we can go farther back than that:

Climate Forcing

GHG or greenhouse gas forcing, represented by the green line, has largely departed from the typical natural cycle of the past 800,000 years. This is not a natural event.

Over the past 100 years, we have been consistently increasing our production of these heat-trapping gases, such as carbon dioxide. Notice the correlation to the temperature index. It is extremely unlikely that the GHG forcing is being caused by anything other than humans. We are simply the only thing that has dramatically changed our output of these gases in this time scale.

Why does this upward trend in temperature matter? Well, at the moment we've been cozy in our coastlines for quite some time, but that might be changing soon

Glacial melt has been increasing dramatically recently, most notably since 2004. Though there is a regular melt-freeze cycle that normally balances the ice loss in the summers, the increase means that the ice can't be replaced fast enough. Additionally, as more ice melts, it triggers factors that only accelerate the process. One of these is the decrease in reflectivity--snow is extremely reflective, which partially shields the glaciers from the sun's energy. However, as the composition of the glaciers is changed by rapid melting, more of this heat is instead being absorbed as the reflectivity decreases. Another is meltwater--as the glaciers melt the runoff drains down and is actually creating a slippery layer between the ice and the land, encouraging parts the fragmenting ice shelf to slide into the ocean. The more these factors occur, the faster the ice melts and moves off the land, which only contributes back to them, creating a positive feedback loop. Because of this loop instead of sea levels rising at a constant pace, the rate is actually accelerating. Scientists estimate that by the year 2100 sea levels will rise as much as 23in, affecting millions of coastal populations. 

However, the strain of global warming won't be felt exclusively by these people. Rising temperatures and sea levels will also cause: changes in weather systems and frequency of extreme weather events, decrease in freshwater and water quality, land erosion, flooding from increasing evaporation, out of control wildfires and drought from over-dried land, food scarcity from affected agriculture, not to mention the ruin of the economy from all the damage to the infrastructure and massive loss of jobs and human life....

What can we do about it? seems like really the best we can do is stop contributing to the speed of the process as much as possible. It's already been set in motion, we can only try to slow it down. 

Global warming amirite

Sunday, October 4, 2015

2001: A Pacing Odyssey

2001: A Space Odyssey is a very unique film. It manages to combine beautiful artistic shots with semi-realistic physics. It was a little hard to sit through at 2 hours and 40 minutes, only because it's not the sort of movie I'm used to watching. It likes to show instead of tell, unlike many modern movies. This leads to long cuts and lingering spacescapes, with minimal dialogue. It's a movie you have to go into expecting it for what it is; more of a statement than a solid, linear narrative. Reading another review on it, the reviewer commented on how when seeing it in the theater, many moviegoers were frustrated by not immediately understanding the progression of events. It was not made to be ultra accessible like many modern films--it's not incredibly difficult to grasp, but you have to think on it and consider the artistic decisions that Kubrik made to get a sense of what it's suggesting. He completely forgoes explicit statement of anything.

The actual plot explores the progression of human evolution. In the beginning, an ape discovers the destructive power of a bone, crushing an animal skeleton and sending bits flying everywhere. Its brutal work done, it sends the weapon catapulting into the air and the movie immediately cuts to a similarly-shaped space station swinging around the earth. It easily parallels these two things just by clever directing. The monolith first appears in this earliest part of human development. The next place it is found is deliberately buried on the moon. When this one is discovered by humans, the sunlight hitting it causes it to transmit a powerful radio signal, aimed towards Jupiter. This is the basis for the Jupiter mission. Five scientists are sent on a spacecraft towards the mysterious destination of the signal. Accompanying them is a HAL 9000, a highly intelligent computer entity that controls many of the basic functions of the ship. Supposed to be infallible and incapable of error, the two crew members not in cryogenic sleep call his reliability into question when he gives them differing information from mission control. This spirals into a sequence of events ending in all the scientists but one, David, being terminated by HAL. David escapes towards the monolith only to be sucked into a vortex of colors, landing him in a room where he experiences accelerated aging, finally finding himself in bed as an old man, reaching towards a final monolith at the foot of his bed. He is transformed into a celestial, godlike baby.

This movie is surprisingly much more true to physics than many of the other movies we've viewed so far. Though next to Armageddon, anything will look pretty decent. They captured centripetal force and the basics behind effective artificial gravity fairly well. The crewmembers feel gravity evenly throughout their bodies because relative to the radius of the huge space station, their height is inconsequential. In a smaller spacecraft, such as the Russian station in Armageddon, the rotation would have a dizzying effect because as you move closer to the center the force decreases, so your head and feet would be experiencing drastically different rates of rotation. The film also is rare in that it accurately depicts the silence of space--sound waves travel best through dense materials and space is about as far from dense as you can get (one atom/cm3, compared to 20 million trillion atoms/cmon earth).

I really liked the movie for its beautiful shots and thought into the artistic composition. However, I feel like the careful artistic composition could have still been retained even if some of the shots had been cut in length slightly. There was a solid five minutes spent solely on an aerial view of the moon shuttle moving them across the surface to their destination. You really have to be determined to enjoy this movie for the experience of it. Like your ex-girlfriend; pretty but difficult to love.

ISMP rating: GP
My rating:  3/5

Monday, September 28, 2015

Superspeed and Other Powers I Wish I Had: A Report

In the chapter Flash Facts - Friction, Drag, and Sound, James Kakalios examines the possibility of the crazy physics of the Flash, the supersonic superhero who, after lightning strike laboratory incident, gains the ability to travel incredible speeds. This in turn opens up a surprisingly diverse set of talents for him..

The most basic one is building-scaling. The author found that it is actually possible for the Flash to run up the side of a building. If you disregard the insane speed necessary to perform the feat, the physics mostly check out....mostly. In order to travel the vertical distance of the building, he needs to have a high enough velocity to overcome the gravity that pulls at him in the opposite direction, which can be put into the equation v2=(2gh). James Kakalios compares this to an earlier chapter on Superman, where to reach a height of 660ft, he would need to have an initial velocity of 140mph. This wouldn't be a problem for the Flash who can run near light speed.

However, one of the most important forces to the Flash in order for his power to be relevant is friction. Without friction, he could windmill as much as he liked and wouldn't get anywhere. One particular villain with ice powers was able to incapacitate him this way. In order to travel up the side of the building, he needs enough friction to propel him forwards, vertically. However this in itself is a problem because friction is proportional to the weight being exerted perpendicularly on a surface, and as the Flash runs up a wall, none of his weight is acting down into the wall. Technically there can't exist any friction and so his powers are negated.

This problem is solved by examining his stride length for the speed he's traveling. Friction becomes barely relevant when you realize that his feet would only touch the ground once every 660ft if he's traveling a mere 3600mph or 5250ft/s. This alone is enough to cover the height of the building in the Superman problem, between footfalls.

Regardless, he would get smashed into the side of the wall from the force of the sudden 90 degree change in direction.

Another thing the author examines is the realism in the physics of the Flash's famous ability to run on water. It turns out that water has a high enough viscosity that it doesn't have time to move out of the way of his feet. Similar to how falling into water from a height is always described as feeling like hitting cement, the impact is so sudden that it creates a high density region where there is contact with the water. It acts more like a solid at the speed that the Flash travels at. There is still the issue of gaining momentum through friction, but it could be possible if he created backwards spinning vortices similar to how a water-strider propels itself.

Kakalios, James. "Flash Facts - Friction, Drag, and Sound." The Physics of Superheroes. New York: Gotham, 2005. 57-68. Print.

Sunday, September 20, 2015

Avoiding Death by Shockwave

A major meteor impact event is inevitable in Earth's future. There's 150 million asteroids over 100m orbiting just in the inner solar system. Luckily for us, thanks to NASA's NEAR program and other scientific efforts, all asteroids over 1km have been cataloged, and they're working to track all asteroids over 140m by 2020. However, to give perspective on this, the Tunguska event's object, which leveled over 80 million trees over an area of more than 700 miles is estimated to have only been 30m. Something of a relatively minor size compared to what is tracked could easily devastate a large area. Given, the Earth is mostly water, and chances are that it would never hit anywhere remotely populated, but if 30m can devastate an area that large, the 150 million over 100m are a considerable threat.
There are several legitimate asteroid deflection strategies that have been proposed by NASA, ranging from nuclear detonations to gravity tractors.

Despite the ridiculous plot of Armageddon, they kind of got right the part that nuclear detonations are the most effective logistically out of all the methods. Depending on the situation, it could work better to either detonate it by flyby, on the surface, or subsurface. The important part is to not fragment it though--we have good enough detection systems that it would (likely) never be as close of a call as it was in Armageddon, and the point is to push it off trajectory, not split it into several pieces of matter that have several different paths. The "astronauts" in Armageddon were lucky that their space rock was not in fact a collection of space rock rubble held together by gravity, which would have exploded and become atmospheric buckshot.

The point of the tracking systems is to have warning enough to change the course of a dangerous object. We don't currently possess anything that could release the amount of energy required to significantly alter the course of a large asteroid if it's already close to Earth. A nuclear detonation could best be used to change the change slightly change its path that over time it would miss our little planet.

Kinetic impact would be the next most effective. This is essentially launching something at the object to knock it off course. Of course, it has to have enough mass and velocity to even affect the object. The average asteroid orbits at a speed of 25km/s, or 55,900mph. The fastest spacecraft we have to date, New Horizons, reached a top speed of 40km/s after being assisted by Earth's orbital motion, but quickly dropped off in speed to around 19km/s by the time it reached Jupiter.

However, its mass is only 478kg, which would be utterly useless in stopping a medium asteroid such as 25143 Itokawa, which is has a diameter of about 400m and a mass of 3.5x1010kg. It would barely change its course.

The Deep Impact mission, which drove a 370kg impactor into Temple 1, a comet with a mass of 7.2x1013 at a speed of 28.6km/s affected the comet as to cause a 0.0001 mm/s change in its velocity and decrease its perihelion by 10m. However, if this same impact had been delivered to a comet 125m in diameter, in 10 years it would be moved by one radius of the Earth, or 6741km. So kinetic impact would be an effective deflection method, and we have the technology to execute it, if we have enough warning. The larger the object, the more time we need to significantly alter its course.

However, any unexpected celestial bodies and we're screwed.

Sunday, September 13, 2015

A Study of the Messiness of Death by Rail Gun

The year is 1996. The movie, Eraser. The muscles and guns hero....Arnold Schwarzenegger.

So Arnold is at the warehouse, and decides to give the Bad Guys a taste of their own creation. That is, violent death by railgun. But how realistic is the violence, for both parties involved?

First, we want to find out exactly how much firing one of those hurt.

With the law of conservation of momentum, we can use the equation:

Where a=Arnold and b=bullet

So for the values, I found:

Ma= 113kg (the Governator is reported to weight about 250lb)
Mb= 0.1kg
Vi,a= 0m/s
Vi,b= 0m/s
Vf,a= ?
Vf,b= 1.80x108m/s (I interpreted "near the speed of light" as 60% of the full 3x108m/s)

To calculate Arnie's final velocity:

Since the left side zeroes out, we can rearrange the equation to
Vf,a = -MbVf,b M

Fill in the fun parts
Vf,a = (0.1kg)(1.80x108m/s) / 113kg
the kgs cancel out to give the final units of m/s

And this is his final velocity
Vf,a 1.6x105m/s

While only traveling at 0.05% of the speed of light, that's still 356,078mph and probably won't feel good even in his smithereened state.

yeah that's gonna hurt

Next, we find out what this feels like to be on the receiving end.

Where v=Victim and b=bullet

Mv85kg (these guys didn't look too hefty)
Vf,v/b= ? (determined as one value if we're assuming the bullet stuck and they traveled together)

The equation for this
V(Mv + Mb) = MvVi,v+MbVi,b

Arranges down to
Vf  = MbVi,b Mv + Mb

And with the values plugged in
Vf  = (0.1kg)(1.80x108m/s) 85.1kg

Vf  = 2.1x105m/s
The victim is sent flying by the projectile from the rail gun at a speed of 2.1x105m/s, or 472,819mph......ouch.

Conclusion: This movie was not depicted nearly as violently as it should've been.

Saturday, September 5, 2015

Mission Impossible: Trying to refer to Tom Cruise as anything other than Tom Cruise is pointless

1. In the bridge attack scene, Tom Cruise quickly assembles his G36 just in time to shoot down the drone that's coming in for a second pass at him, after missing the first time to annihilate his car. He looks over a large hole blown in the road, the only ground remaining obstructed by a flaming wreck, to see The Bad Guy about to escape onto a helicopter. He takes off on a short running start, tosses his gun, and barely clears the gap, sliding and catching the edge. While Tom Hunt is known for performing many almost certainly impossible feats, is this one of them? Useful things to know are his velocity at takeoff and the distance of the gap. Tom Cruise claims he can run 17mph and while this is almost certainly not true, it's plausible for his character. As an athlete it is possible to reach maximum speed within 4-6 strides and he takes about 7. The gap is about the width of 7 tires, assuming they're about 26" in diameter that makes it 4.6m wide. In this past olympics, 11th place in the women's long jump was given to one Ivana Spanovic with a distance of 6.35m. Another thing to consider is that while Tom Cruise may occasionally act like a tank or some sort of invincible armored car, he doesn't behave like one in accelerating straight over drop-offs. His jump gives him a little more vertical lift as he crosses. Given this, the amount of acceleration he has, and as an adult male in good physical condition, it is possible that he would have made this jump.

2. Another question of physics comes up with the jump/swing scene. Tom Cruise is desperate to get his wife back, desperate enough to do some literal sketchy math and decide he can reach the top of his target building simply by swinging from a taller building next to it, effectively making all of Bad Guy's security measures useless. We're given all sorts of relevant information, such as his target building (B) is 162m, his swing point (A) 226m, and the buildings are separated by the strangely exact distance of 47.55m. The difference in height is 64m. With some basic trigonometry you find that to reach a cable in a straight line from the fulcrum point of building A to a point straight across on the roof of building B would require it to be 80m. Tom Cruise most likely calculated for it to be a little shorter so that he didn't become abstract window paint. The physics question remaining out of this would be: can he reach a high enough speed from his starting angle, when the rope first snaps taut after his jump, to carry him far and high enough to not simply fall short and slam back into building A? Important factors for this would be his speed, the distance along the path of the arc that the angle (about 130 degrees) creates, and possibly his mass? With some more math I found that the arc length is about 216m. At this point I'm fairly sure this turns into a 2D kinematics problem (hopefully for Tom Cruise's sake not a collision one) where you treat his initial freefall and the swing separately to calculate the speed, however attempting this I got straight up lost so I'll leave it as a posed question. To the inexperienced eye he appears to impossibly speed up in the second half of the arc on the upswing when they cut between shots but only physics can truly determine exactly how stupid desperate Tom Cruise was here.

3. The last scene I chose was the helicopter chase scene. They are escaping after a successful rescue mission of soon-to-be creepy-eyes-dead-lady, but are being pursued through a field of wind turbines by an Apache helicopter armed with among other things, heat-seeking missiles. After several close calls the pilot of Tom Cruise's helicopter decides to kill them all by flying through a turbine, just kidding, it's a tricky evasive maneuver and the Bad Guys fall right for it, flying through after them and not being able to perform a similar not-dying stunt. So the question is: can they really be that stupid or is there some typical movie trickery going on that makes the Bad Guys always lose? And the actual physics question is: at the velocity they were following at, and the timing of the blades, should the Apache helicopter also have made it through the turbine? Appropriate values to find would be the velocities of both helicopters, the distance through the turbine, and the speed of the blades. None of these are available or easily calculable in standard measurements so I will be using approximations. Up until this point, the Apache has been matching team TC's copter, never more than 2-3 seconds behind. The speed of the blades is approx. one rotation per second. The first helicopter takes exactly this second to fly through, the next blade actually looks like it should come down on the tip of the tail. The Apache, approaching the turbine at an identical velocity, takes almost three full seconds to pass through from the exact same point. The third blade crunches with a satisfying explosion directly into the middle of the helicopter. It's not possible for the helicopter to have slowed down that quickly from the speed they were pursuing at (Apache top speed is 182). If I had actual values to plug in I would find this clearly violates some kind of minorly super important stuff, like the basic laws of motion.