Laws of motion question?

Question

if a lighter arrow is shot through the air with the same amount of force as a heavy one which would go farther and faster,

Answer 1

I would say the heavier one.  It would have greater mass, and would be less affected by wind resistance due to its inertia

Answer 2

A heavy arrow would go slower an not so far, because the same energy has to move a higher mass. The force of the impact would be the same in both, but the lighter arrow will go faster and farther

Answer 3

I assume the arrows have the same shape and size.

Force is the rate of change of momentum. So, if you use the same force, you will get the same momentum. Of two arrows with the same momentum, the lighter arrow has a higher velocity, because the momentum is the product of mass and velocity p=mv.

So, the momentum at start is the same. The drag forces don't depend on the mass of the arrow. However gravity depends on the mass. The havier arrow will go down earlier.

So the surprising result is: if you don't have strong headwind, the lighter arrow should go farther and faster.

Note that the lighter arrow may do less damage in the target, because the penetrating power depends on the density. And, also, drag depends on the speed, therefore the lighter arrow will lose more momentum due to drag.

Further note that it may be hard to apply the same forces to the two arrows. If you use a bow, the velocity of the chord may be limited by drag and friction. Due to the higher velocity, the time that the arrow has contact with the bow is shorter. If the time of the force acting is shorter, the momentum will be less.

For these reasons weapon projectiles are not made of light material, usually.

Answer 4

The lighter arrow will go farther.