Our equation weāre going to work with here is F*d = 0.5 * m * v^2
we want to solve for velocity, so thatāll turn out to v^2 = (F*d)/(0.5*m)
so according to some quick google research, the amount of force it takes to pierce skin is between 10 - 20 Newtons, so weāll go to 15N because the skin of the palm is a bit more tough. That gives us F = 15N, which will probably be our only fixed point number, because the rest Iām going to have to assume.
Distance is going to be fun, because, well, look at this shit
That is an entire magma river (and then some) away! Forget the velocity, what the fuck is your aim, Blue??
So I will admit I am shit at trying to gauge distances, but Iām gonna do my best. So first up, Iām going to say that the Links are manlets at the height of 5ā² 2ā³ (thatās botwās Linkās height, so admittedly Iām being a little more generous than the supposed canon heights nintendo gave, because in the game engine botw Link is 5ā² 2ā³ and I like that measurement more), which in Not American Units is 157cm, or, to keep all of our units from getting messy, 1.57m. Using the very precise science of taking a Link and measuring how many silhouetted Links it takes to get to Vio, which in this panel we have about 5 silhouettes away (give or take) which would give us 1.57 * 5 = 7.85m, which will be our distance measurement, d=7.85m (side note: if anyone has a better way of measuring this distance let me know bc again, this is the one thing Iām shit at).
itās a little baby pebble! so letās assume that this pebble is made out of granite (itās on a mountain and the mountains near me are granite so there), is a sphere, and is baby. So to find the mass of it, weāre going to need another formula! This time, weāll use density to relate to our pebbleās volume and mass, orĀ Ļ=m/V which simplifies to m= Ļ*V. Our V will assume a perfect sphere because I said so, so V = 4/3 * Ļā * r^2. For our radius, I will use my small hands as a reference, and funnily enough, 0.5cm seems to fit the radius of that blood mark, so r = 0.5cm, or, to keep our units straight, r = 0.005m. Thatāll make our volume V = 4/3 *Ā Ļā * (0.005)^2 => V= 5.24*10^-7 m^3. For our density, weāll just be using the density of granite, so Ļ = 2691 kg/m^3. Our mass, then, will be m = (2691 kg/m^3) * (5.24*10^-7 m^3) => m = 0.00141kg.Ā
Sweet! We have all the numbers we need now, so letās plug them in:
v^2 = (0.5m) / (F*d)
v^2 = (15*7.85) / (0.5*0.00141)Ā = 117.75 / 0.000705
v^2 = 167021
sqrt(v) = sqrt(167021)
v = 408.68 m/s
which if you go to easier units to visualize thatās 912 mph!!!
For reference: most MLB pitchers have an average of 97 mph for each pitch.Ā
For other reference, you have to go 770 mph to break the sound barrier.
So either Blue can chuck something incredibly accurate at 10x the speed of an MLB pitcher and break the sound barrier, or itās just magna magic. You decide on how magical he is.
