## Sunday, September 13, 2015

### Eraser

In the movie the Eraser Arnold Schwarzenegger's character is attempting to stop the sale of a newly developed rail gun to the Soviet Union. This rail gun is able to shoot aluminum bullets at the speed of almost the speed of light, which is about 3 x 10^8 meters per second. In one scene, Arnold has control of a rain gun and shoots an enemy in the chest and he goes flying. The question is, was how far the enemy flew accurate? Also, how far should've Arnold flown back when he did shoot the gun?

First, we must start with the before and after of Arnold shooting the gun. The formula we will be using will be (Ma)(Vfa)+(Mb)(Vfb)=(Ma)(Via)+(Mb)(Vib) where Ma is mass of Arnold. Vfa is Velocity final of Arnold. Mb is Mass of bullet. Vfb is Velocity final of bullet. Via is Velocity initial of Arnold. Vib is Velocity initial of bullet.

Lets say the mass of the bullet was .01 Kg since the movie didn't inform us of some of the specifics. We will put Arnold at about 110 Kg. Obviously the initial velocity of both the bullet and Arnold are 0. And, since the movie stated "close to the speed of light we will put it at around 3x10^7 meters per second.  All we need is the final velocity of Arnold. So that math will give us Vfa=-(.01Kg)(3x10^7m/s)/(110Kg). This gives us that Arnold will fly back at the speed of around 2727.27 meters per second. This proves that despite how large Arnold is, he would not have been able to hold his ground with this gun.

Now the before and after for the enemy. We will switch every "a" in the formula to an "e". We will also state that the bullet is lodged and stuck in the enemy so the enemy and the bullet have the same final velocity. So that gives us (Me)(Vfe)+(Mb)(Vfb)=(Me)(Vie)+(Mb)(Vib). Me will be 80 Kg. Mb is still .01 Kg. Vib is still going to be 3x10^7. And Vie is 0 meters per second. That will give us
Vfe=(.01Kg)(3x10^7m/s)/80Kg. That would make the enemy fly back at a speed of about 3750 meters per second. While the enemy did fly back very far, its just not quite far enough for good old physics.

#### 1 comment:

1. The movie was set in the mid-1990's - after the dissolution of the Soviet Union. The guns were being sold to Russian black market arms dealers. Anyway, you made one small mistake. You need to remember to divide by the mass of the enemy AND the bullet at the end. Remember, the bullet lodged in the enemy when he was hit (at least that's our assumption). It's a small factor, but I want to be sure you know how to do these problems correctly.