The
nonlinear vector-valued differential equation ma = -mg j - b|v|v controls
the flight of a projectile subject to quadratic air resistance. Here
m is the mass, g is the force of gravity, b is the constant of air resistance,
j is a unit vector directed upwards, v is the velocty vector, |v| is
its magnitude, and a is the acceleration vector.
Sliders
at bottom select values of m and b , as well as the initial speed v0
and angle up from horizontal, θ0 .
The initial conditions can also be selected by a mouse click on the
graphing window.
Initiate
an animation by pressing [throw] at lower right, stop it by pressing
[stop], and resume it by pressing [continue].
In
the graphing window, the flight path is depicted in white. The projectile
is represented by a red dot, and the animation leaves behind a trail
of red dots at equal time increments. The initial velocity vector is
indicated by a blue arrow, the force of gravity by an orange arrow,
and the resistant force by a yellow arrow.
A
cursor rollover produces crosshairs and a readout of the x and y coordinates.
©
2007 P. Dourmashkin, H. Miller and J.-M. Claus