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2016•JOURNAL OF ADVANCES IN PHYSICSOpen access

Simple analytical algorithm for constructing the envelope of the projectile trajectories in midair

Peter Chudinov, Vladimir Eltyshev, Yuri Barykin

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Abstract

A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. The air drag force is taken into account asthe quadratic resistance law.An analytic approach is used for the investigation. Simple analytical formulae are used for constructing the envelope of the family of the projectile trajectories. The equation of envelope is applied for the determination of the maximum range of flight. The motion of a baseball is presented as an example.

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What this paper is about

A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. The air drag force is taken into account asthe quadratic resistance law.An analytic approach is used for the investigation. Simple analytical formulae are used for constructing the envelope of the family of the projectile trajectories. The equation of envelope is applied for the determination of the maximum range of flight. The motion of a baseball is presented as an example.

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Available abstract

A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. The air drag force is taken into account asthe quadratic resistance law.An analytic approach is used for the investigation. Simple analytical formulae are used for constructing the envelope of the family of the projectile trajectories. The equation of envelope is applied for the determination of the maximum range of flight. The motion of a baseball is presented as an example.

Key concepts: Projectile, Envelope (radar), Projectile motion, Drag, Trajectory of a projectile, Range of a projectile, Simple (philosophy), Quadratic equation

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