Introductory Programming
Fall 2005

Evaluation 6 Today

Today's instructions

1) create a file named freefall.m in the usual place you put scripts

2) type in the following code

function dxdt = f(t, X)
r = X(1);      % the first component is position
v = X(2);      % the second component is velocity

drdt = v;                          
dvdt = acceleration(t, r, v);

dxdt = [drdt; dvdt];    % pack the results in a column vector
end

function a = acceleration(t, r, v)
g = 9.8;      % acceleration of gravity in m/s^2
a = -g;
end

This is similar to what we worked on last time, except that
X is a vector with two elements: position and velocity.

The function dxdt unpacks X, computes drdt and dvdt, and
then packs the result into a vector.

The function acceleration computes the acceleration of a
hypothetical particle under force of gravity.  Notice that
acceleration is (in general) a function of time, position
and velocity.

3) evaluate dxdt from the command line using the
   values t=0 (seconds), r=4000 (meters), v=0 (m/s)

   Assuming that it works, what does the result mean?

4) use ode45 to compute the position and velocity of the
   particle over a time range from 0 to 10 seconds, with the
   initial values t=0 (seconds), r=4000 (meters), v=0 (m/s)

   How long does it take the particle to fall from 4000 meters
   to the ground?

5) Modify acceleration to compute the force of wind resistance
   for a 70 kg skydiver with drag constant c = 0.22.

   What is the skydiver's terminal velocity?  How long does 
   he/she take to bounce?

6) Modify acceleration again so that after 30 seconds of free-fall
   the skydiver deploys a parachute, which (almost) instantly
   increases the drag constant to 2.7.

   What is the terminal velocity now?  How long (after deployment)
   does it take to reach the ground?