Module for Projectile Motion

Numerical Methods for O. D. E.  using Mathematica. (c) John H. Mathews, 2003

Preliminaries.

The following mathematical models for projectile motion are considered.

Model (i). No resistance yields  

    .  

Model (ii). Resistance proportional to velocity yields  

    .  

Model (iii). Resistance proportional to the square of the velocity yields  

    ,  for the ascent,
and
    ,  for the descent.  

Example 1.  An arrow is shot upward from the origin with an initial velocity of  300 ft/sec.
Assume that there is no air resistance and use the model  .  
Find the velocity and position as a function of time.
Find the ascent time, the descent time, maximum height, and the impact velocity.

Example 2.  An arrow is shot upward from the origin with an initial velocity of  300 ft/sec.
Assume that air resistance is proportional to the velocity, ,
and use the model  .  
Find the velocity and position as a function of time, and plot the position function.
Find the ascent time, the descent time, maximum height, and the impact velocity.

Example 3.  An arrow is shot upward from the origin with an initial velocity of  300 ft/sec.
Assume that air resistance is proportional to the square of the velocity,  ,
and use the model  .  
Find the velocity and position as a function of time, and plot the position function.
Find the ascent time, the descent time, maximum height, and the impact velocity.

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