## Sunday, September 6, 2015

### Impossible Physics, The Movie

~~~~~~~~~~~~~~~~~~~~~~~~~Question 1~~~~~~~~~~~~~~~~~~~~~~~~~

How long of a rope would Agent Hunt need to swing from an adjacent building to the building where the Rabbits Foot is being held?

Towards the end of the movie, Agent Hunt must swing from an adjacent, taller building, to the building across the street in order to infiltrate through the roof. Luckily for anyone who wants to know the possibility of this, the measurements of the buildings and the distance separating them are given to us in the previous scene. The list of measurements needed to find the length of rope needed are below:

Difference in height of the two buildings = Building height #1 - Building height #2
=    226 meters   -   162 meters
=                 54 meters
Distance between the two building = 47.55 meters

If we use the Pythagorean theorem, we will be able to calculate the angular length of rope needed to cover from the top corner of Building 1, to the top corner of building 2. Below is a figure explaining the situation.

So to solve the equation:        h2   +   d2   =   l

(54)2   +   (47.55)2   =   l2

l2   =    5177 meters

l   =   72 meters

So, for Agent Hunt to be able to swing from the corner of the first building to the corner of the second building, his rope would need to be just over 72 meters long (to accommodate for his height).

~~~~~~~~~~~~~~~~~~~~~~~~~Question 2~~~~~~~~~~~~~~~~~~~~~~~~~

How much heat would it have taken to melt the side of the armored truck?

During a chase scene, thermite is used as chemical reaction to melt the side of the armored truck, so that the squad can steal the rabbits foot inside the vehicle. The list of measurements needed for this question are below:

Heat capacity of the metal of the truck = C
Change in temperature = ΔT
Mass of sample = m
Amount of heat transferred = q

So, after a few brief internet searches, I found that the metal used for the armored truck is tempered steel. Tempered steel has a heat capacity of .490 kilo-joules per kilogram per kelvin. The change in temperature is the temperature of the ignited thermite (2500 degrees Celsius or 2773 Kelvin) - the temperature of the air that day (295 Kelvin on a normal day). The mass of a 1 in x 1 in x 1 in piece of steel weighs .283 lbs or 128 grams. For this question, the size of the piece of steel melted is assumed to be 24 in x 24 in x 1 in.

C = .490 kJ/kg/K
ΔT = (2773-295) = 2478 Kelvin
m = (128 grams)(24)(24) = 73700 grams or 73.7 kilograms
q = ?

So, to solve the equation:        q=mCΔT

q = (73.7kg)(.490kJ/kg/K)(2478K)

q = 89500 kJ

So for the thermite to have actually melted the side of the armored truck, it would have had to have created 89500 kilo-Joules of heat energy. This does not seem likely...

~~~~~~~~~~~~~~~~~~~~~~~~~Question 3~~~~~~~~~~~~~~~~~~~~~~~~~

How fast would Agent Hunt had to have run to make it to his wife in the given amount of time during the final chase scene?

After calling the evil guy and getting the address of his wife, Agent Hunt sprints towards the location to save her. He is being directed by his tech savvy friend on the other end of a phone. He runs there super quickly. The needed measurements are as follows:

Distance ran = d
Time spent running = t
Average speed = v

After re-watching the scene. The distances given to Agent hunt by his tech friend add up to 2220 meters. This added to an additional 100 meters for unspecified running reaches 2300 meters ran by Agent Hunt. After timing the scene, it was determined that Agent Hunt ran this far in 68 secs.

d = 2300 meters
t = 68 seconds
v = ?

So, to solve the equation:         v = d/t

v = (2300 m) / (68 sec)

v = 34 meters/sec

So, in conclusion, for Agent Hunt to have been able to run that far, that fast, he would have to have been running at 34 meters per second. I think Tom cruise should quit acting and compete with Usain Bolt in the next Olympics.

#### 1 comment:

1. I like the use of the Pythagorean theorem to analyze the first scene. One thing you didn't mention in that scene is at what angle did he start his swing. We can calculate from your triangle the angle at which he needed to finish the swing. I'll talk on Monday about why this is important. Incidentally, the thermite wasn't used to steal the Rabbit's Foot; it was used to free Owen Davian. But I like the thermal physics example.