2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/86442A classical problem of mechanics involves a projectile fired from a given point with a given velocity whose direction is varied. This results in a family of trajectories whose envelope defines the border of a 'safe' domain. In the simple cases of a constant force, harmonic potential and Kepler or Coulomb motion, the trajectories are conic curves whose envelope in a plane is another conic section which can be derived either by simple calculus or by geometrical considerations. The case of harmonic forces reveals a subtle property of the maximal sum of distances within an ellipse.Also available from http://democrite.in2p3.fr/democrite-00023173Physics EducationClassical Physicstext