Mission Impossible 3 Analysis



The Mission Impossible movie series is full of action scenes where main character Ethan Hunt, played by Tom Cruise, gets himself out of many tricky situations using his weapon skills and combat mastery. He is also depicted as a math guy; seen writing physics equations in order to plan out his next move under intense pressure. Although the physics behind the movie is not the only area of critique, there are three scenes that stood out to me specifically that challenged the laws of physics.


Scene One: Tom Cruise Launches into Car




Video should start at 4:50 to see explosion scene

In this scene I am perplexed about Tom Cruise's direction of motion when experiencing the explosion from the missile impact. Is his direction of motion physically possible? 
The force of an explosion is an area vector (perpendicular to the surface of the explosive). I have drawn the area vectors below to show the direction of the force that Tom Cruise should have experienced due to the explosion below.




The  explosion force vectors in the diagram above represent the direction that Tom Cruise should go according to newtons second law ΣF=ma, where the net force's direction determines which way Tom Cruise should go. According to the diagram, Tom Cruise experiences only a single force which is directed straight downwards. That being said, when he lifts off of the ground, he should have moved in that same direction.
It appears that there is no net force that acts on Tom Cruise in the direction of his movement. This does not check out![-]

In the scene, Tom Cruise is just passing the middle of the white car as the explosion hits and he ends up just past that point when he makes contact with it. This car is a dodge stratus which is approximately 192" in lengh. He seems to have moved about half the distance of a door which is about 24 inches. It appears that he is about five feet from the car at the time of impact which is about  60 inches. Using basic trigonometry: 


The angle Φ which is about 68.2 degrees west from the force vector represents the incorrect path that Ethan Hunt traveled in the scene.



Scene Two: Tom Cruise Cruising from Building to Building in Shanghai


In this scene, Tom Cruise is on the top of a building in Shanghai and wants to get to another one as quickly as possible. In order to do so, he attatches a cable to himself from a pulley that has the cable spooled around it. Is it really possible for Tom Cruise to reach the height of the next building? Tom Cruise is falling for 13 seconds before the pulley runs out of cable and the tension in the cable keeps him supported. To determine the answer to this question, we would need to use conservation of energy.

What we would need to measure:
  • The downward velocity of Tom Cruise
  • Distance fallen
  • The angle the cable makes with the pulley when the pulley runs out of cable,
  • The length of the cable,
  • The height he reaches above the other building

Velocity:



Distance Fallen :


Angle:

Angle When Taut

Length of cable:

Height he reaches on other building:





Conservation of energy: 



The initial and final energy of Tom Cruise consists solely on his potential energy at both positions since his downward velocity is close to being perpendicular to the circular path of his cable swing. 

Potential energy = mass(m)*acceleration due to gravity(g)*height(h)


From the diagram above, his initial height is much smaller than his final height. 

So,


Thus, his journey from one building to the other was not possible. [-]



Scene Three: Tom Cruise Destroys Mile Record


During the latter half of the movie, Tom Cruise is in Shanghai and is trying to find his wife. While desperate to find her, he calls one of his friends who works in intelligence at the Impossible Task Force control base. He learns that he needs to run about a mile through busy streets in order to get to her. 

The elapsed time that it takes him to run one mile is about one minute and fifty seconds. At what speed must he run in order to accomplish this stunning mile time? 

What we need to measure:
  • Distance (given)
  • Time (time from when he started running to when he stopped)


  • One mile = 1609.34m
  • One minute and fifty seconds is equal to 110s.

1609.34/110 = 14.6 m/s = 32.7 mph

The man had to run 32.7 mph. The movie shows him stopping many times for cars and people so he was not always running. For comparison, Usain Bolt runs 27.8 mph without stopping. This does not check out. [-]



Overall rating of the movie: [-] [-] [-]



































Comments

  1. Wow! Great stuff. Good to see so many equations. Some of your links appear to be broken. Make sure your blog looks like it's supposed to before you finish. I'd also like to see you working in metric units consistently in the future, so please convert inches and such. I like that you picked the explosion scene; lots of students miss that. For the rating, I want you to put it on the ISMP rating system.

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