Predicting How to Hit a Moving Target.

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SUMMARY

This discussion focuses on calculating the angle required for a turret to hit a moving target in a two-dimensional space without external forces. The recommended approach involves converting to polar coordinates to simplify the calculations of the angle (θ) and distance (r) as functions of time (t). Utilizing the law of sines and cosines is also suggested for determining the necessary angle based on the projectile's velocity. The discussion emphasizes the importance of accounting for the target's movement to accurately compute the lead angle.

PREREQUISITES
  • Understanding of polar coordinates and their applications in physics.
  • Familiarity with projectile motion and velocity functions.
  • Knowledge of trigonometric laws, specifically the law of sines and cosines.
  • Basic calculus concepts, including derivatives and integrals.
NEXT STEPS
  • Explore the application of polar coordinates in physics problems.
  • Study projectile motion equations and their derivations.
  • Learn how to apply the law of sines and cosines in dynamic scenarios.
  • Investigate advanced calculus techniques relevant to motion prediction.
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Mathematicians, physicists, game developers, and engineers involved in trajectory calculations and motion prediction.

Unit978
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In a two dimensional ideal world without any external forces acting on an entity, if i were to have a turret that fires projectiles at a known velocity towards a moving target at a certain distance away at an angle with respect to the x-axis, what calculation would be needed to compute the angle necessary between the target and the turret to hit the target with the projectile.
 
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Can you write down a formula for the distance to the target from the launcher's starting position as a function of time?
 
Go polar?

Depending on what your velocity function looks like, you'll probably want to convert to polar coordinates, as it makes it easier to find the rate at which θ is changing as the turret tracks the target. r(t) and θ(t) Or just work it out as a triangle using law of sines/cosines. You'll need to divide r at time t by the linear velocity of the projectile, and figure that 'lead' into the angular equation. Might be a simple derivative or integral involved. Haven't thought it far enough through to say for sure.

If you're still stumped tonite, post up again and we can work it out on paper.
 

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