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Now, you have a gun with a fixed muzzle velocity. The gun is being carried by something with a velocity on the x and y and acceleration on the x and y. How would I go about solving the angle required to hit the target at any given time?

The velocities and accelerations are not constant, but can be produced at any given time.

I'm basically looking for a kick in the right direction of the things I will need to know to figure this out.

Thanks.