Calculating Trajectory and Force of Bow & Arrow

[Stratosphere]

I want to find out the trajectory and the force of my bow and arrow. I was wondering how I could actually do this. I know how to calculate the force and kinetic energy of the arrow but I don’t know how to plot out the path of the arrow in flight I thought I might have to use Kinematics but I am not sure.

P.S This is NOT homework I am simply curious to see how far my arrow will go without testing it on a field, plus its more fun to use physics.

Also in working out the force of 2 different arrows I used to measure which one is better, I got that arrow 1 with a mass of .0285kg has a total of 11.721 joules of force and my heavier arrow of .05kg has a total KE of 14.1 joules. Is this right? I figured that they would be the same amount of KE because it is being shot with a constant force from the bow string.

 

[Loren Booda]

I would be interested in the effect of fletching and center of mass on deviating the arrow's path from the first-order parabolic.