Predicting How to Hit a Moving Target.

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In a two-dimensional scenario without external forces, calculating the angle for a turret to hit a moving target involves using polar coordinates to track the target's position over time. The formula should express the distance to the target as a function of time, incorporating the known projectile velocity. Utilizing the law of sines or cosines can help in determining the necessary angle. Additionally, the relationship between the target's distance and the projectile's linear velocity must be considered to account for the lead required. Further collaboration can assist in refining the calculations if needed.
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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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