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DYNAMICS - CASE STUDY

    Introduction


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

    vx = 400 ft/s       vy = 400 ft/s
  • The aerodynamic drag force is given by

     
    Question

   

What is the trajectory of the projectile for

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

   
  • 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.