BALLISTIC TRAJECTORY

The nonlinear vector-valued differential equation \(m\overrightarrow{a} = -mg\hat{j} - bv\overrightarrow{v}\) controls he 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, \(\hat{j}\) is a unit vector directed upwards, \(\overrightarrow{v}\) is the velocity vector, v is its magnitude, and \(\overrightarrow{a}\) is the acceleration vector.

Sliders at bottom select values of \(m\) and \(b\), as well as the initial speed \(v_0\) and angle up from horizontal, \(\theta_0\). The initial conditions can also be selected by a mouse click and drag 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