PC 253: Quiz

ODE I Quiz

Modify the galileo.py program to solve the two-dimensional projectile motion problem with air resistance. Assume the projectile is a 6.0 kg cannonball (radius = 5.50 cm) shot at a 45° angle with an initial speed of 50.0 m/s. Use the Euler-Cromer method to numerically solve the ODEs. Test your program to make sure it works by comparing the results of the program without air resistance to the known resistance using the two-dimensional kinematics equations with constant acceleration. This is most easily done by setting Cd = 0 in your program.

When you are sure your program is working correctly, use it to create a plot showing the trajectory of the cannonball with air resistance and the trajectory without air resistance using the two-dimensional kinematics equations. What is the range of the cannonball with and without air resistance?