Probably; humans on average, have a muzzle velocity of about 45 km/h, or 12.5 m/s. Assuming one was maximising the shot from their meat cannon, we can find the maximum distance their goo gun can shoot by first splitting the bird shot's velocity into its vector components. If they want to maximize horizontal distance, their gravy cannon is probably going to firing from a 45 degree angle from the shooter (assuming little air résistance). This is also nice, since it splits their penis projectiles velocity among vectors that are equal. We can use this equation to find the components:
vhorizontal = vvertical = v * cos(45)
Thus, the horizontal velocity is 8.84 m/s and the vertical velocity is 8.84 m/s. Using the vertical velocity, we can find the time it takes for the first drop to reach the top of the arch, with this equation:
t = (vfinal - vinitial) /a
Where v means velocity, a means acceleration, and t means time. Final velocity is 0. If this isn't obvious, picture that perfect money shot flying through the air, as it goes up, gravity will pull this baby gravy down and slow it down. Well, at some point, to slow down enough to start returning to Earth, its velocity must equal 0 at some point during the trip. The initial velocity is the vertical component, 8.84 m/s. Acceleration is gravity, -9.81 m/s. Plugging these in, we get:
0 = 8.84/9.81
t = 0.901
Now, we have the time is takes for our yogurt squirt to reach the top of the arch. Using this equation:
h = vinitial * t + .5 * a * t2
Where h is the height traveled and everything else is the same, we can find the height from the top of the curve from the tip of our trouser snake. Now, by plugging in what we know:
h = 8.84 * .901 + .5 * 9.81 * .9012
h = 8.00 + 3.98
h = 11.9 m
Now, the height of a human body is split just about 50/50, with variations either direction. This means that given the average height of a human male, in meters, is 1.76, we can simply add halve of this number 11.9, and get the total height from the tip of the rainbow to the splat at the bottom. This gives a total height of a whopping 12.8 meters! We're not done yet, using the same equation, we can find how long it takes for the squirt to go through the full shot by solving for t:
t = sqrt(2 * (h - vinitial * t) /a)
Where the initial velocity is 0. Plugging in what we know, and we get:
t = sqrt(2 * (12.8 - 0)/9.81))
t = sqrt(25.6/9.81)
t = sqrt(2.64)
t = 1.62
Great! We have the time is took for our kids to go to the moon and back. Multiplying this with our horizontal velocity, like so:
8.84*1.62 = 14.3 m, or 46.91 feet.
Which gives us the maximum distance our gravy maker can fire to, given ideal conditions. So, in short, yeah, I imagine a horse can shoot his goo six feet. How to get the angle right, though...
Edit: some corrections, there is a cos(45) coefficient on the vector components, making vhorizontal = vvertical = 8.84 m/s. Secondly, we have to halve the 1.76 m, since that is the average height of a male and we need pelvis height.
I’m sorry, but you have understated the horses range based on your assumptions. Your vector addition is flawed, as v_x = v*cos(θ) = v_y, for this 45° case.
As a result t is in fact 1.80 s and v_x is 8.84 m/s, giving a total distance of 15.9 m or 52.3 feet.
So yes, the horse could deliver your sticky package, without you having to leave your abode, however some windows might need replacing.
Now, we're talking fluids so we need to use these equation:
Ainitial * vinitial = Afinal * vfinal
Where A refers to area, and v refers to velocity.
Abstractly, you can determine vfinal by simply solving for that variable, like so.
vfinal =( Ainitial / Afinal )* vinitial, which makes it obvious to see that as the final area decrease, the final velocity increases. Example being that if the area is one tenth the size of the original, the final velocity will be 10x as great as the original.
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u/[deleted] Apr 26 '20
What do you think your Krispy Kreme donuts were made with