How to calculate the speed and direction to intercept with a target


I need to find a way to calculate the required speed and direction to intercept with a target given the target’s current position, speed and direction.

could anybody help me with this problem ?

thanks for your help in advance.

I think you have to use vectors.
You have 2 vectors [a,b] and you need the result 3 [r].

Vectors represent a position or a speed

If you pick up actual position and last position of an object you get the actual speed and direction. Use this vector for starting

You know the distance between you and the target, and this can be yous as second vector.
Use trigonometry to resolve the equitation.

in a 3d space is much more complex
r = square root of ( (xx) + (yy) + (z*z ))
can be usfull to get the speed and direction vector.

start in 2d is much better.
Imagine to intercept using a 90° angle or triangle (this can help). Then you can use Sin or cosine.
A triangle has 3 angles.
In this case you can choose for starting that one angle is 90°.
So is simple to get the other 2 [Alpha1 , Alpha2 ]. And then the final Vector. Example r = a / sin of Alpha

When you finish please edit and expand this answer as you wish.