How is Misaka's railgun so destructive? In episode 1 of Railgun, Misaka's railgun up-ends a good chunk of what appears to be an olympic-sized swimming pool. Later in the same episode, it is revealed that her railgun travels at a velocity of 1030 m/s.

However, the numbers don't add up.
Suppose Misaka uses 10 gram coins. At 1030 m/s, that coin has this much energy:
Energy = 1/2 m v^2
       = 1/2 (0.01 kg) (1030 m/s)^2 = 5304.5 kg (m/s)^2
       = 5304.5 Joules

An olympic-sized swimming pool has 2,500,000 kg of water. Based on the image above, that cone probably travels a good 100 meters into the air.
So let's say for benefit of the doubt, that only 10% of the water is lifted 100 meters into the air.
Energy = m g h
       = (0.01 * 2500000 kg) (9.8 m/s^2) (100 m) = 2.45 * 10^8 kg (m/s)^2
       = 2.45 * 10^8 Joules

The coin needs 2.45 * 10^8 Joules of energy to uplift the swimming pool as shown above. But her coin can only provide 5304.5 Joules. There is a difference of about 4 orders of magnitude.

Okay... Before anyone dismisses this as just another case of Anime physics, let's look at what else could produce so much energy:

The spin of the coin is not captured in the net velocity of 1030 m/s. But given the moment of inertia of a little coin, it would need a tremendous (relativistic?) amount of spin to carry 10^8 Joules.
The charge of the coin is unspecified in the Anime. Perhaps Misaka somehow polarizes the charge in the coin and somehow makes it release upon contact with the target.
The mass-energy (E = mc^2) of the coin is 9 * 10^14 Joules. Is this what she did?

So the question is: Is there any official explanation for where the coin gets so much energy? Or are we left to dismiss this as another case of Anime physics?
According to the anime and manga, Mikoto has a "muzzle velocity" of 1030 m/s:



In contrast, the US Navy's railgun has a muzzle velocity of 2520 m/s (~5600 mph or ~7.5x the speed of sound), with a muzzle energy of 10.64 megajoules (10.64 million joules). Which is probably comparable to the amount of energy in an average-sized car moving at 250 mph.

Comparatively, the an AK-47 rifle has a muzzle velocity of 715m/s (~1600 mph or ~2x the speed of sound), with a muzzle energy of ~2010 joules (assuming 7.62x39mm cartridges are used, but may vary depending on the type of ammunition).

While not very impressive stat-wise as far railguns go, since actual railguns are capable of achieving speeds of possibly more than ~5000 m/s. Take note that Mikoto is a middle-schooler that can fire eight shots of these per minute, which is on par with "typical" railguns.

Assuming the coin comparable to the size and weight of a U.S. quarter, one can assume that the coin she uses has a weight of about five grams. Using this formula we can get he muzzle energy:


  Energy = 0.5*(mass)(velocity)2 = 0.5*(0.005kg)(1030m/s)2 = ~2652.25 joules


So Mikoto outputs a bit more damage than an semi-automatic assault rifle.

But that's not what we're seeing now is it? 



Not quite. But what could cause such a difference in output?

According to Page 1, Chapter 4 of the Railgun manga, she manipulates electromagnetism to achieve her results. This seems plausible since if the magnetic field were sufficiently focused, she could theoretically accelerate only the coin and/or nearby objects.

Now lets take a look at the pool test again, from the pool cleaning episode (S1, ep. 2) we have an approximate estimate of the dimensions of the pool:

 

Lets measure things in terms of Kuroko's height (~152cm)!



Seeing as the pool doesn't taper or either end, lets assume that the pool is about 14 Kurokos long or ~21.28 m (yes it does seem kinda small), and about 11 Kurokos wide, or ~16.72 m, by the lines on the pool floor and a bit less than ~0.9 Kuroko, or lets say 1.36m deep.

As for the displaced water, we could attempt to integrate the volume of the plume of water, assuming it's half and half air, find it's weight, etc. But we'll be lazy here and assume that 1/1000th of the pool water volume was dispersed into the air when Mikoto fires her railgun. The pool would have a volume:


  Volume = (1.36 m)*(21.28 m)*(16.72 m) = ~486.73 m3 of water


Since the "center of mass" the plume of water seems to be comparable be near the top of the gymnasium-type building, going be an eye estimate of the door compared to the building lets assume that it's 10 m tall. In order to calculate the energy needed to achieve something like this we do:


  (Energy it takes to lift an object) = (mass of object)*(acceleration due to gravity)*(lift altitude). 


In this scenario let us cut a bunch of corners and assume that all the energy of the shot goes into lifting the water (by which ignore the energy spent warming the water up, creating the sounds loud explosion, any dramatic winds effect), then we have


  Energy = (1/1000)*(~486.73 m3)*(1000 kg/m3 water)*(9.8 m/s2)*(10m) = ~47699.54 joules


If we plug it backwards into the kinetic energy equation:


  √[(~47699.54 J)*2 / (0.005 kg)] = ~4368.04 m/s


So the muzzle velocity of her railgun would be ~4368.04 m/s.

One can only assume that, since we must respect the canon value of 1030 m/s, that perhaps the damage caused by Mikoto ability is due to her manipulation of electromagnetic caused as the coin moves through the air or some other factor... But then again, what do we know about the physics of this world where Science and Magic co-exist?