MATH FAIR HELP NEEDED. Learning trajectories using a bow?

Trajectories are the path the arrow takes, so a project would look at the forces acting on the arrow.
e.g. if you fire the arrow horrizontally out over a flat field, how long does it take the arrow to hit the ground? does it matter how hard the arrow is fired? how does it compare to the time it takes an arrow to hit the ground if just hled horizontally and dropped. In al lcases, if lift is negligible, the time to hit the ground should be the same as gravity is the only force acting downwards and accelerating the arrow in that direction. It will travel further forward if fired harder, but always hit the ground in the same amount of time.
You could also plot the distance travelled versus the angle the arrow is shot at into the sky.. Always draw the bow to the same distance, make a simple gauge to measure the bow's angle to gorund (e.g. a plumbline and some graph paper), what is the optimal angle for distance?
How does wind affect the optimal angle - on windy days should you fire at a lower or higher angle to get the longest distance?
How does a cross wind affect the flight? How much do you need to aim left or right of a target to compensate for a certain windspeed - a simple anemometer is cheap and would give the windspeed.
As a test, measuring the windspeed you should then be able to predict what angle to fire an arrow to hit a given target at a given range - i.e. to predict the trajectory.

Trajectories are parabolas, more or less. You could do a set of experiments to show that a firing angle of 45 degrees will give the maximum range - assuming the bow draw is the same for each shot. You could also do a set of experiments at a given angle and measure the range for various amounts of bow draw. Use a spring balance to measure the bow draw force.