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So I have two objects, Target and Interceptor. Target's position, direction of movement and movement speed are known, and Interceptor's position and movement speed are also known. Both movement speeds are fixed, and Target will never change course. Both are moving in three dimensions; Interceptor can move in any direction.

I want to figure out which direction Interceptor needs to move in, at its fixed movement speed, to be able to collide with Target as Target moves, as quickly as possible - or, as the case may be, I want to know if it is impossible for Interceptor to collide with Target.

I don't know how to do this, and my Google searches clearly haven't been using the right search terms, because nothing useful comes up. How do I calculate this?

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If the targets velocity is V and the interceptors desired speed is S:

  1. Calculate the normalized vector U between the interceptors current position and the targets current position Tp - Ip.
  2. Find a such that the length of Vi + aU equals S. aU is the desired speed.
  3. It will take distance / (Vi + aU).length time to intercept.
  4. If you get a negative value for a then they will never intercept.
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