Mission Impossible III

Scene 1: Humpty Dumpty

To break into the Vatican, Ethan Hunt must successfully get over the walls surrounding the city. After  scaling the outer wall, Ethan falls to the other side safely, thanks to his spy equipment which was attached to the top of the wall. The physical question I am trying to answer in this scene is, what was Ethan's final velocity as the wire catches him before he goes splat. The equation I will be using is vf2 = vi2 + 2ad. The relevant quantities I would need to answer for this question would be; initial velocity, acceleration, and distance. Ethan’s initial velocity is 0 m/s, because he was laying on top of the wall before he fell. The acceleration is -9.8m/s2 because that is the standard acceleration due to gravity. Before Ethan fell to the other side of the wall, he measured his distance from the ground and got 16.55 meters. The wire caught Ethan about .25 meters above the ground, so the distance he traveled was 16.30 meters. With these quantities I am able to calculate how fast Ethan was traveling as his equipment had to catch him, which is 17.9 m/s.

Scene 2: The Fulcrum

In this scene, Ethan swings from one skyscraper to another to retrieve the rabbit’s foot. The physical question I am trying to answer in this scene is whether or not this swing is possible. A few of the relevant quantities I would need to answer this question were conveniently given to me from the movie. The height of the first building is 226 m. The height of the building Ethan is swinging to is 162 m. The distance between the two buildings is 47.55 m. Ethan’s acceleration would be -9.8m/s2 due to gravity. We know his initial y velocity is 0m/s, but to answer the problem we would also need his initial x velocity. Ethan has a running start as he jumps off of the first building. The maximum speed a human can run is 28 mph, or about 12.5 m/s. Because Ethan is a spy and not an olympic record holder, it can be appropriately assumed that the speed he ran off the building was around 9 m/s. The time as depicted in the movie for Ethan to jump from the one building, swing, and land to the second was about 25 seconds. With the height of the two buildings, the distance between them, the acceleration due to gravity, both his initial velocities (x and y), and the time frame, the last factor we would need to find was the length of the cable he swung from. With all these quantities it could be solved whether or not Ethan’s fulcrum could be successful in real life.

Scene 3: A Run Through Shanghai

After being captured by the bad guys then escaping, Ethan has to save his wife, Julia. He calls Benji, the computer guy, to locate his location and tell him how to get to Julia. Benji tells Ethan that he is 1 mile, about 1609 meters, Northeast from Julia’s location. In the movie, it takes Ethan around 110 seconds to get to the other location. The physical question I am asking is how fast would Ethan have to be running to travel 1609 meters in 110 seconds assuming he is at a constant speed. This is easily calculated by dividing the distance traveled by the time it took Ethan to get there. Ethan would have to run 14.62 m/s, or roughly 32 mph, to get to Julia’s location in that time frame. As stated in the last problem, the maximum speed a human can run is 28 mph, so it is safe to say that this scene from Mission Impossible III, is truly impossible.