Parabola of safety
Encyclopedia
In classical mechanics
and ballistics
, the parabola of safety or safety parabola is the envelope
of the parabolic trajectories
of projectile
s 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 reproved 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.
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
and ballistics
Ballistics
Ballistics is the science of mechanics that deals with the flight, behavior, and effects of projectiles, especially bullets, gravity bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.A ballistic body is a body which is...
, the parabola of safety or safety parabola is the envelope
Envelope (mathematics)
In geometry, an envelope of a family of curves in the plane is a curve that is tangent to each member of the family at some point. Classically, a point on the envelope can be thought of as the intersection of two "adjacent" curves, meaning the limit of intersections of nearby curves...
of the parabolic trajectories
Parabolic trajectory
In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1. When moving away from the source it is called an escape orbit, otherwise a capture orbit...
of projectile
Projectile
A projectile is any object projected into space by the exertion of a force. Although a thrown baseball is technically a projectile too, the term more commonly refers to a weapon....
s shot from a certain point with a given speed
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...
at different angles to horizon in a fixed vertical plane. The fact that this envelope is a parabola
Parabola
In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface...
had been first established by Evangelista Torricelli
Evangelista Torricelli
Evangelista Torricelli was an Italian physicist and mathematician, best known for his invention of the barometer.-Biography:Evangelista Torricelli was born in Faenza, part of the Papal States...
and was later reproved by Johann Bernoulli
Johann Bernoulli
Johann Bernoulli was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family...
using the infinitesimal calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
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.