This Exercise Set has been submitted for peer review, but it has not yet been accepted for publication in the PICUP collection.

Introduction to Projectile Motion: Target Practice

Developed by Sean Bartz

This program lets students create an animation of a ball undergoing projectile motion and then use an analytical calculation to attempt to hit a target.
Subject Area Mechanics First Year * Students will use the Euler or Euler-Cromer method (see instructor's guide) to create an animation of projectile motion to see how the motion depends on initial conditions (Exercise 1) * Students will compare analytical results to the results of computation and use this to hit a target with a projectile (Exercise 2) * Students will generalize the derivation of the range calculation to cases where the target is not at the same height as the launch height of the projectile (Exercise 3) 40 min
**Exercise 1: Computational solution of projectile motion** Use the Euler or Euler-Cromer method to simulate the projectile motion of the ball. Try a few initial values for $v_0$ and $\theta$ to get a feel for the results. Analytically find the horizontal displacement for a ball that is launched with $v_0=5.00$ m/s and $\theta = 60.0^\circ$. Use your program to check your results. Do the results match exactly? What are some possible sources for any discrepancy? How can you improve the agreement? **Exercise 2: Comparison with analytical results** Using the code produced in Exercise 1, try hitting a target 0.50 meters to the right of the launch point. * By hand, find what launch velocity will hit the target for a launch angle of 60 degrees. * Use your program to check this result. You should be able to get within 1 cm of the target. * By hand, find what angle will hit the target for a launch velocity of 4.0 m/s. *Hint: there are two angles that will work* * Use your program to check this result.