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So once again I will point out that you got the right answer but for some reason you refuse to accept your own answer! Your attitude is really strange.

It is not a simple vector sum.

If I drive my car in a straight line

Why not?

You cannot accelerate a mass by pushing at right angles to its motion.

You cannot accelerate a mass by applying force at right angles to its line of action.

My answer is now and always has been, from the start that the blue ball does not change speed. It moves at 4 units before and after the collision.

the blue mass moves on the line of CD an unchanged speed of 4 units and also along the line of BC at speed of 3 units.

collision the blue ball is moving at 5 units along the new line of travel,

is an expression of your belief, it has no basis in science

Perpendicular force.Changes the velocity of a moving massBy changing the direction of the mass.It is also known as centripetal force.

The only force acting on the blue mass cannot increase its speed.The speed of the blue mass remains as constant as any other mass subjected to a perpendicular force.

What is the speed of the blue ball along its direction of travel?

Please supply any sources that support your claim

the posts where I state. The speed of the blue ball does not change

That is Dark Motion.

your ideas are wrong

It is also moving at a speed of 4 units in an as yet undetermined direction.

Which bit is wrong?