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Related Concept Videos

Projectile Motion: Example01:18

Projectile Motion: Example

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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...
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Motion of a Projectile01:23

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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.
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Consider the gas molecules in a cylinder. They move in a random motion as they collide with each other and change speed and direction. The average of all the path lengths between collisions is known as the "mean free path."
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Projectile Motion01:20

Projectile Motion

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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...
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Projectile Motion: Equations01:26

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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.
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Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:
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Enhanced projectile path estimation using multi-vehicle FMCW radar sensors.

Amgad A Salama1,2, Mahmoud A Hussein3

  • 1The Research and Development Centre, ADC, Cairo, Egypt. amgad.salama@acm.org.

Scientific Reports
|February 2, 2026
PubMed
Summary
This summary is machine-generated.

Multi-vehicle Frequency-Modulated Continuous Wave (FMCW) radar formations significantly improve projectile path estimation. A four-vehicle setup reduces estimation errors by 75%, enhancing active protection systems.

Keywords:
Active protection systemsFMCW radarMulti-vehicle sensingPath parameter estimationProjectile trackingSensor fusionSignal processing

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Area of Science:

  • Radar Systems Engineering
  • Defense Technology
  • Signal Processing

Background:

  • Accurate projectile path estimation is critical for military vehicle active protection systems.
  • Existing single-sensor approaches have limitations in precision and robustness.
  • Frequency-Modulated Continuous Wave (FMCW) radar offers potential for enhanced sensing.

Purpose of the Study:

  • To develop and evaluate a multi-sensor FMCW radar approach for improved projectile path estimation.
  • To quantify the accuracy gains in key path parameters (range, time, velocity).
  • To assess the feasibility of near-term deployment using existing technology.

Main Methods:

  • Implementing a distributed multi-vehicle FMCW radar sensing network.
  • Applying advanced signal processing techniques for data fusion.
  • Conducting detailed simulations to analyze performance against single-vehicle systems.
  • Validating theoretical predictions of triangulation benefits.

Main Results:

  • A four-vehicle formation demonstrated approximately 75% error reduction in projectile path parameter estimation.
  • Significant improvements observed in pass range, pass time, and velocity accuracy.
  • Triangulation from multiple sensing positions proved robust for linear trajectories.

Conclusions:

  • The proposed multi-sensor FMCW radar approach substantially enhances projectile path estimation accuracy.
  • This advancement offers practical benefits for improving military active protection systems.
  • The methodology is compatible with current FMCW radar technology and data fusion algorithms, enabling rapid deployment.