-I'm assuming the time the acceleration acts on the bow, and on the sling is the same, meaning, the peak force and acceleration while would not let me figure out, how fast the arrow flys, but I know that the sling bullet would have to leave with the same force, to travel the same distance
No offense, but you're very confused about what a force is, and how it differs from the work done by a force.
-0.1 metres is 39 inches
"0.1 meters = 3.93700787 inches"
You're right on the 0.1 thing. I meant to use equivalent to 39 inches. I just hit the wrong button, easy fix. I actually just realized that.
The only way you're gonna understand this is if I just give an example. Say the force from the bow and the sling both act on the arrow, and bullet for the same amount of time. We know the Mass of the arrow, and the force the bow will impart. Equal, opposite reaction not going over that. F=MA like in the picture we can find the acceleration would be 23500 m/s squared. We want to find out how fast it's going to go, we can put any number in, and it will still make this valid, because the time is the same in both, I'll use 1 second. Velocity = Acceleration X Time, so 23500 X 1 = 23500 m/s. The thing we have to figure out now is how long it's gonna take that arrow to fall. I'm gonna ignore maximum velocity for both cases, because I assume they would be similar anyways. I'll shoot them both straight, and both from a metre high. Acceleration of gravity, 9.81. distance = starting velocity X time + half the acceleration X time squared, so 1=(0X Time) + (9.81 Time squared)/2, which goes to square root of 2/9.81= time. Which is 0.45 seconds and a billion more numbers. So now we know the time of flight 0.45, and the velocity 23500 m/s. This is pretty basic now. If it's going 23500 m/s in 0.45 seconds it will go 10575 metres. Now we have a distance for the sling to beat. And we know the mass of the bullet, yes I've researched this, and I've actually used a sling. 0.05 kg. We know it's gonna travel for 0.45 seconds, again this is basic physics. You should already be able to tell it's gonna have to be traveling at the same speed as the arrow, to get as far. So we then can go back and find it's starting acceleration. Again it would have to be over the same time, already determined. Which I picked 1 second. Velocity=Acceleration x Time, which gives us 23500=Ax1. So we got an acceleration of 23500 m/s square. Hmmm sounds familiar. If we use F=MA we got 23500X0.05= 1175 newtons, 262 pounds of force on the end of that string. Now whats the force the bow had 470 newtons of force, or 105 pounds. We now know the mass of the bullet, the force, and the radius, from earlier. Correction it as 1 meter we have and here, you'll notice my actual mistake, which is the only thing you didnt. 1175=(0.05X Vsquared) /1. Which confusing parts out equals a velocity of 153 m/s. Which is doable. Nether the less, the slings were usually made of flax, hemp, and wool. Which I'm doubting could easily withstand 262 pounds of force for lengths.
So, I was wrong, but not for anything you said. Which doesn't matter much, cause I just wanted to see if it was possible for a sling to out shoot a bow, and I did. It's possible if you have it made out of something strong.
I know perfectly well what force is. And I know what work is. I'm just assuming you understood the relationship I'm trying to show.
