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firemeboy · Daedalian Member

Hey all, I have another problem for the masters. I have a friend who makes Bows and Arrows. We are going to go out and shoot them for fun. We want to calculate the speed at which they are traveling. Let us put aside the problem of how fast they are traveling horizontally right now, I want to figure out how fast they are traveling vertically.

Because they are sefl bows (bows made out of one piece of wood), they are not as quick as some of the high tech bows of today. When you fire at a target, you often have to aim high. The arrow travels up, and then comes to a stop (in it's vertical movement of course), and then begins falling. I can't remember the formula to find the speed of an object falling. I am assuming that we can time the arrow leaving the bow, and then add the speed of the arrow falling from the sky. What we are going to do is time how long the arrow falls from it's highes point.

So, do I have faulty logic here, and if not, what formula would I use...?

Thanks

Fire

ps, We are not trying to be exact here, so I don't need to figure air resistance unless it is incredible easy.

Ghost Post · Icarian Member

I guess it all depends on what you mean by speed here. The vertical velocity of the arrow is not constant. It has a downward acceleration due to gravity of about 9.8 meters per second squared. Are you just looking to find the average velocity of the fall? That would be dependant on how high up the arrow was when it began falling.

firemeboy · Daedalian Member

Maybe I am not sure what I want.

If I shoot an arrow and it leaves the bow at 150 feet per second, how would I figure out how fast it was at the top of the arc, and then how fast at the time it hits the target. Ignoring air resistance, would it be faster, slower, same when it hit the target?

Ghost Post · Icarian Member

Ignoring air resistance, etc, we see that the horizontal component of the velocity is constant from the time the arrow is released to the time that it hits the target. When it is released it has some vertical velocity upward. At the top of the arc it has zero vertical velocity. When it hits the target there is some vertical velocity downward.

So, it is going slowest when it is at the top of the arc. The speed will be greater at which ever of the starting point and ending point is lower. If the target is at the same level as the arrow was when it was released, the arrow will be going the same speed when it hits the target as when it leaves the bow.

firemeboy · Daedalian Member

Thanks Drew.