Homework #1
Instructions. This is due on September 5
at the beginning of class. It is worth 10 points. Late papers lose 2 points per
day late. You must work by yourself, but feel free to consult with me. Explain
what you did and why you did it: good explanations are essential! Your paper
should have an introduction, a main body and a conclusion. Start early, ask
questions and do well.
Introduction. The first day of class we
developed a model of a falling object based on the assumption that air drag is
proportional to the square of velocity. In the book (see pages 2-3), the model
of a falling object does not include the square. Which model is correct depends
on the object and on how fast the object is moving. In this assignment, we
start to explore how much difference there is in the two models.
Problems. Consider the following two
models of the velocity of a falling object.
(a) dv/dt = 9.8 - 0.7v
(b) dv/dt = 9.8 - 0.05v2
Show that the positive equilibrium (terminal
velocity) is the same in each case.
Compare and contrast direction fields for the two
equations.
At first glance, does it seem that it matters much
which model is used?