Originally posted by King Kandy
I understood the point, I was just trying to show how stupid this thread is.
Awwwwwwww. 🙁
To answer the question:
Why, the speed would scale up to the c, of course!
If we assume a power level is linear in quantity and we use the 150,000,000 number for Goku, we can use that energy comparison to see how close to c Goku can get. Keep in mind that the closer to c you get, the more energy it requires. It requires an infinite amount of energy to actually reach c so an enormous amount of energy may very well get him to c. You have to use the Lorentz Factor to get the proper energy required for C.
We could calculate the energy required to both accelerate and maintain that constant speed (because the "atmosphere, which we could assume is at STP, would exert a resistance force against Goku as he flew. This constant is technically not constant as the density is varied but for the sake of simplicity, we could average that out to just STP.) So it would be an initial acceleration vector work = force * delta distance.
That plus the force required to keep the system in motion against the resistance force of the air.
Using the Lorentz factor in the 28 hour flight time is not needed and this is why: We know that Goku was able to greatly reduce the actual distance traveled to get across snake-way because he just jumped in a straight line down snakeway on his way back home. So it's not truly 621,371 miles. I did an eyeball guess with some cords I had on my desk and it looks like the snaky pattern amounts to double the length of a straight line. Goku flew, remember? He bounced and flew..but let's just assume 310,685 miles.
He flew 310,685 miles in 28 hours, right?
He did it before at a power level of 5000 (And, initially, he did the hundred+days trip at a power level of a little over 460, not 1000, like you suggested, because he died and was resurrected.)
So it would be an initial acceleration vector work = force * delta distance.
That plus the force required to keep the system in motion against the resistance force of the air. You have to use the drag formula WITH the previous formula in order to get total energy expended.
force of drag = (1/2)*density of fluid*velocity of the object in the fluid*drag coefficient (similar to a friction coefficient...it's basically the coefficient for a given object in a fluid)*orthographic projection area (this sounds complicated, but it's not. It's basically the cross-sectional area of a sphere...but for a human body, it would be a bit more than just the orthographic projection area due to the dynamics experienced by the clothes "flapping" through the fluid(atmosphere).
Anyway, what is the average velocity of Goku at 310,685 miles at 28 hours travel time? 11,095 mph. That's not fast enough to have to incorporate the Lorentz factor because it's not even percent of the Lorentz factor. It's ~.0017% c. We will probably get there when we scale up to 150,000,000.
I do not feel like doing the math but I've provided all the necessary equations and concepts needed to carry out the calculations. Someone else do it as I can't be arsed to spend an hour working this out.