ChoRyuJin hauls GaoGaiGar out of the deep sea, of a depth of 10,000m (or 10km).
STORY|勇者王ガオガイガー
君たちに最新情報を公開しよう!『勇者王ガオガイガー』Blu-ray BOX発売決定!! Division 1:2015年11月25日発売/Division 2:016年2月17日発売
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Firstly, ChoRyuJins hooks reach 10,000m deep at astoundingly fast speeds, finding and rescuing his fellow Braves in just a few seconds.
T = 1s/30
= 33.3333333ms X 2
= 66.6666666ms + 4s
= 4.06666667s
T = 10,000m/4.06666667s
= 2459.01639/340.29
= Mach 7.22623759
It takes longer hauling GaoGaiGar up as it's a heavy machine, but even that is done in short time.
T = 33.3333333ms X 11
= 0.366666666s + 27s
=27.3666667s
T = 10,000m/27.3666667s
= 365.408039/340.29
= Mach 1.07381363
Of course, being a huge heavy machine, GaoGaiGar would weigh quite a bit. And it does, having a mass of 264.2 tons (or 264200kg)!
KE = (0.5)mv^2
= (0.5) X 264200 X 365.408039^2
= 1.76383929e10 joules
= 4.2156770793499 tons of TNT
If that's not enough, it's possible to go for an even higher yield, as GaoGaiGar is being pulled through water, which is far more viscous that air. The viscosity of water is 8.90e-4 Pa*S (or kg per m^2), while the viscosity of air is while the viscosity of air is 1.81e-5 kg/m^2.
8.90e-4/1.81e-5 = 49.1712707
Ergo, water is 49.1712707 times more viscous than air, and it would take 49.1712707 times more energy to move through water at such speeds (you can see this with bullets, which quickly loose momentum underwater).
E = 1.76383929e10 X 49.1712707
= 8.67302192e11 joules
= 207.290198852772 tons of TNT
This isn't the only impressive feat in this episode!
GaoGaiGar and EI-10 sink at incredibly fast speeds, and we even have the distances measured (about 1000m)!
T = 33.3333333ms X 6
= 0.2s + 3s
= 3.2s
T = 1000m/3.2s
= 312.5m/s
Final Results
ChoRyuJin's hooks find GaoGaiGar = Mach 7.226
ChoRyuJin hauls GaoGaiGar to the surface (speed) = Mach 1.074
ChoRyuJin hauls GaoGaiGar to the surface (energy - low end) = 4.216 tons of TNT
ChoRyuJin hauls GaoGaiGar to the surface (energy - high end) = 207.290 tons of TNT
GaoGaiGar sinks to the bottom of the Marina Trench = 312.5m/s