Parabolas of Safety
Suppose a projectile is thrown from the center of the coordinate system with initial velocity at angle with the x -axis. The motion of the projectile in vacuum is demonstrated by the applet below. When the angle changes randomly from 0 to we obtain a family of parabolas with the same initial velocity. The envelope of the family is a parabola with vertex , focus at the origin , and - intercepts .
- To simulate the motion, click the "Animate" button or dragg slider n.
- Click the "Show Foci" checkbox to see the focus of the parabolas as they are constructed.
- Click the "Locus of the Foci" checkbox to see the locus of the foci of the parabolas.