Projectile Motion of an Arrow: The Ideal Shot

by Taylor Heyen

Submitted : Fall 2015

This project seeks to find the angle above the horizontal that an archer has to aim to achieve maximum distance, to determine the impact velocity, and to measure the length of the trajectory of the arrow. We used basic algebra, calculus, and physics to achieve this goal. The specifications of the bow and arrow were considered when determine the initial velocity of the arrow. We begin by modeling the trajectory of the arrow, with the help of an excel spreadsheet, using the formulas and equations of projectile motion and trial and error to find the appropriate angle. Once the appropriate angle was found we then tracked the velocity of the arrow on that trajectory, and measured the length of the arc created by the trajectory. The angle to achieve maximum distance with our given conditions was found to be 45 degrees above the horizontal. The impact velocity of the arrow was found to be equal to the initial velocity and the length of the arc was found to be 654.403 meters. In addition to finding out the specific knowledge we sought, the data provided information on altitude, distance, and velocity at any given time during the flight. I found this to be an effective method of answering my questions for an idealized model. To find more real world applicable solutions we would have to repeat the calculations factoring in drag, wind variable, and any rotation of the arrow during flight.

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