A Physicist's Guide to Mathematica, 2nd Edition

Chapter 4. Mechanics

Falling Bodies

The Problem

A small body falls downward with an initial velocity v₀ from a height h near the surface of the earth, as in Figure 4.1.1. For low velocities (less than approximately 24 m/s), the effect of air resistance may be approximated by a frictional force proportional to the velocity. Find the displacement and velocity of the body, and determine the terminal velocity. Plot the speed as a function of time for several initial velocities.

Figure 4.1.1. A small body falling downward with an initial velocity v₀ from a height h.

Physics of the Problem

Let the x-axis be directed upward, as in Figure 4.1.1. The net force ...