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Projectile Motion: Equations

Projectile Motion: Equations

Projectile motion is commonly observed in our day-to-day life. For example, a basketball thrown by a player, an arrow shot from a bow, and kids jumping into the pool, all undergo projectile motion.
Any projectile motion problem can be solved by using the following strategy:

Projectile Motion

Projectile Motion

Projectile motion models the flight of an object launched into the air, such as a soccer ball kicked during a penalty, under the simplifying assumption that air resistance is negligible. When gravity is the only force, the object experiences a steady downward acceleration at all times. This single fact explains why projectile motion can be analyzed as two independent motions happening simultaneously: a horizontal motion that does not speed up or slow down, and a vertical motion that continually...

Projectile Motion

Projectile Motion

An object thrown in the air follows a parabolic path under the influence of Earth's gravitational force. The motion of such an object is called projectile motion, and the object itself a projectile. The parabolic path followed by the projectile is called the trajectory. Some common examples of projectile motion are the launching of fireworks, a golf ball in the air, meteors entering the Earth's atmosphere, and the firing of bullets.
When an object falls under gravity and has no horizontal...

Motion of a Projectile

Motion of a Projectile

Projectile motion becomes evident when a player kicks the ball into the air. The launch angle, or the angle at which the ball is kicked, plays a crucial role in determining the trajectory of the projectile. As the ball soars through the air, influenced solely by gravity, its motion can be dissected into two independent velocity components: the horizontal and the vertical.
Horizontal motion, governed by the initial kick, maintains a constant velocity throughout the flight of the soccer ball.

Projectile Motion: Example

Projectile Motion: Example

The theory of projectile motion is very useful for players of several sports to improve their performance. For example, a javelin thrower needs to throw their javelin in such a way that it travels as far as possible. The javelin thrower takes a short run-up to increase the initial speed of the javelin. The range of a projectile is at its maximum at a 45° angle so javelin throwers try to angle their throw as close to 45° as possible.
When we speak of the range (R) of a projectile on level...

Impact: Problem Solving

Impact: Problem Solving

In an experiment conducted during a Mars mission, a rover propels a projectile with an initial velocity, and the projectile rebounds after colliding with the Martian surface. To ascertain the maximum height attained by the projectile after this collision, the known restitution coefficient and acceleration due to gravity are employed.
By designating the launch point as the origin and utilizing kinematic equations, the vertical component of the projectile's velocity at the point of impact is...

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Related Experiment Video

Updated: Jul 19, 2026

High-Speed Optical Diagnostics of a Supersonic Ping-Pong Cannon

High-Speed Optical Diagnostics of a Supersonic Ping-Pong Cannon

Published on: March 24, 2023

Ballistics projectile image analysis for firearm identification.

¹School of Computer and Information Science, Faculty of Computing, Health and Science, Edith Cowan University, Mount Lawley, Perth WA, Australia. d.li@ecu.edu.au

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|October 7, 2006

Summary

Firearm analysis uses unique projectile markings for identification. A new system digitizes and analyzes these marks, enabling precise individual weapon identification, similar to human fingerprints.

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Area of Science:

Forensic Science
Ballistics
Optical Engineering

Background:

Fired bullets and cartridge cases exhibit unique microscopic markings.
These markings can serve as individual "fingerprints" for firearms.
Current methods may lack efficiency and precision in firearm identification.

Purpose of the Study:

To develop a novel analytical system for firearm identification.
To precisely map and analyze the surface topography of forensic projectiles.
To establish a method for individual weapon identification comparable to human fingerprint analysis.

Main Methods:

Utilizing line-scan imaging technique combined with fast Fourier transform (FFT).
Developing integrated optical, photonic, and mechanical systems for surface mapping.
Digitizing and analyzing characteristic markings on projectile specimens.

Main Results:

Successfully mapped the topography of forensic projectile surfaces.
Demonstrated efficient and precise identification of firearms through projectile analysis.
Experimental results validated the proposed system's effectiveness on 16 different weapons.

Conclusions:

The proposed system offers a highly accurate method for firearm identification.
Digitizing and analyzing projectile markings provide a reliable forensic tool.
This approach enhances the capability to identify individual firearms from ballistic evidence.