Parabola of safety

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In classical mechanics and ballistics, the parabola of safety or safety parabola is the envelope of the parabolic trajectories of projectiles shot from a certain point with a given speed at different angles to horizon in a fixed vertical plane. The fact that this envelope is a parabola had been first established by Evangelista Torricelli and was later reproven by Johann Bernoulli using the infinitesimal calculus methods of Leibniz.

The paraboloid of revolution obtained by rotating the safety parabola around the vertical axis is the boundary of the safety zone, consisting of all points that cannot be hit by a projectile shot from the given point with the given speed.


Philip Robinson, On the Geometrical Approach to Projectile Motion, The Mathematical Gazette, Vol. 82, No. 493, 1998, pp. 118–122