Hypersmurf
Moderatarrrrh...
Thurbane said:If any of that is incorrect, please let me know why.
"Therefore the further (higher) it is fired, the more momentum will be behind it when it hits."
That's not the case.
Whatever momentum you impart to it at the instant it leaves the bow (assuming no air resistance effects) is the momentum it will have on impact.
Let's say I fire it essentially straight. It leaves the bow travelling at (say) 100mph. It hits the target travelling at 100mph.
Now let's say I shoot it in a shallow arc. As it travels upward, it slows down due to gravity. At the peak of its arc, gravity has slowed it by 30mph. It's travelling only 70mph. Then it continues on the downward half of the arc, and it accelerates as it travels downward. By the time it reaches the target, it's travelling at 100mph again.
Now let's say I shoot it in a high arc. As it travels upward, it slows down due to gravity. At the peak of its arc, gravity has slowed it by 60mph. It's travelling only 40mph. Then it continues on the downward half of the arc, and it accelerates as it travels downward. By the time it reaches the target, it's travelling at 100mph again.
Now let's say I shoot it straight up. As it travels upward, it slows down due to gravity. At the peak of its arc, it stops entirely; gravity has slowed it by 100mph. Then it starts to fall, and it accelerates as it travels downward. By the time it reaches me, it's travelling at 100mph again.
It doesn't matter how high I shoot the arrow; by the time it reaches the target, its speed (and therefore its momentum) are identical. The height of the arc will influence my maximum range, but not the momentum at the target.
Of course, if the arrows were being fired from the top of a cliff...let's not go there...
No, let's. The arrow will be travelling faster when it reaches the target at the bottom of a cliff than if it reaches a target at the same level as the top of the cliff. But again, how high I arc it makes no difference. If I shoot straight down, straight out, slightly up, or a long way up... by the time the arrow gets to the bottom of the cliff in all four cases, it will be travelling at the same speed.
-Hyp.