While I'm an avid runner and ultimate frisbee is my lifeblood, I still look forward to a singular gym unit each year - archery. Not because I'm particularly good (I'm pretty much always that one person who habitually hits the back tarp), but because I hate changing into sneakers and I do mildly enjoy feeling like Katniss Everdeen.
Physics is embedded in archery. When the string is released, both it and the arrow move forward with a speed dependent on the strength of the bow's wood - a stronger material is harder to draw, but will launch an arrow further and with more force. When the string hits the bow at the top and bottom of the curve, the string slows down a lot, but the momentum continues to drive the arrow forward through the air, letting go of the string and moving towards the target.
Once the arrow is in the air, it enters a state of freefall, all while moving towards the target. It begins to move downward at 9.81m/s2, but the drop is typically negligible given the speed at which the arrow moves. By the time any noticable drop has occurred, the arrow has likely struck its target, hopefully a bullseye.