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 episide, 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
- 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 * 10^14Joules. 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?