Understanding kinetic energy

[pequaide]

aleks: suppose you are sitting on a portion of the Earths surface that is moving 360 m/sec to the east. You have a cannon that can shoot a 1 kg projectile 360 m/sec. If you fire the cannon east the velocity change is from 360 m/sec to 720 m/sec for a momentum change of 360 units of momentum. If you fire the cannon west the velocity change is from 360 m/sec to 0 m/sec for a momentum change of 360 units of momentum. So you can shot deer to the east or to the west, there is no difference in the ballistics of the shell.

If you fire the cannon east the velocity change is from 360 m/sec to 720 m/sec for an energy change of 194,400 joules. This is 259,200 ? 64,800 joules; ? mv?

If you fire the cannon west the velocity change is from 360 m/sec to 0 m/sec for an energy change of 64,800 joules.

So does this mean that you should place your deer blind facing west or does it mean that the Law of Conservation of Energy is false? How can the same powder cause two different changes in energy?

This year our family shot one deer to the east, one to the north, and two to the southeast from our blinds. We made no ballistic corrections for the Law of Conservation of Energy. I guess we shot our deer with momentum.   

Yes; I know there are other planetary motions, but the point is the same.  You should be able to detect a difference if there is one.

[aleks]

Yes; I know there are other planetary motions, but the point is the same.  You should be able to detect a difference if there is one.

That's another paradox with kinetic energy I suppose. 1/2*mv^2 does not cover impulse acceleration: when you are accelerating via small bursts, each burst increases speed of an object (relative to some base) linearly and energy spending is linear as well. On the other hand this is not a violation of laws of energy conservation since the law is built around this 1/2mv^2 (meaning you can multiply anything by another anything, and divide it, and build a system of equations around it, etc). It is only a violation of common sense: while 1/2mv^2 might be working well in closed system of equations, it violates a common sense of understanding of energy spending: if you are doing equal bursts (be it small explosions, ion streams or anything else), each such burst will increase speed of an object by equal value. While e=1/2mv^2 suggests each burst will be adding a decreasing value to velocity (do not forget that each burst takes an equal amount of energy).

But this is not related to my original question.