Problem Diagram

A projectile is fired from a cannon into the air. The initial velocity of the projectile is known. The aerodynamic drag on the projectile is a function of the velocity. Integrating to find a solution for this problem could be difficult... Is there another way?

What is known:

• The projectile is launched from x = 0, y = 0.
• The initial velocity of the projectile is
  
  v_x = 400 ft/s       v_y = 400 ft/s
  
  
• The aerodynamic drag force is given by
  
  

What is the trajectory of the projectile for

1. C = 0.002 ?
2. C = 0.004 ?
3. C = 0.006 ?

• Because the force (and thus the acceleration)
  of the particle is given in terms of the absolute value of the velocity, integration to find position and velocity could be difficult.
• Solve this problem using a method of numeric integration, such as the finite-difference method.
• Drag equation is a vector relationship that needs to be applied in both vertical and horizontal direction.