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