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How can you say the blue ball did not change its speed?

Timing is difficult, if the red ball impacts too early, it strikes the front of the blue ball. This slows the blue ball down and the red ball is deflected forward. If the red ball hits too late, on the back of the blue ball, it speeds the blue ball up and is deflected to the rear.If you hit the blue ball centrally, it neither slows down nor speeds, up and the red ball is not deflected forwards or backwards. It stops.

Yes I see your point.

If this was a simple vector sum then it would be just as you describe.It is not a simple vector sum. The collision is governed by Newton's laws.

Here is the math that says the speed of the blue ball increases

It's over 50years since I did this stuff and since I never had need to use it, I can't remember exactly. I think you look at the conditions at impact and take components of momentum and put mv=m1v1 for both components and solve.

If a force is applied perpendicular to an object's velocity, it will alter the direction of motion without changing the speed.

If a force is applied perpendicular to an object's velocity, it will alter the direction of motion without changing the speed. I think that this applies to a blue ball rolling down a snooker table and struck by a red ball rolling across the table

Do you really think it will carry on along at the same speed?

I keep asking for some maths to show how you think that the collision works out.

consider the collision of two ideal perfectly elastic projectiles

By your assertions, the ball will attain a new velocity of 0.1 m/sec mostly west and will only make it past the edge of the track because it's falling off the tee and not go 200 meters.

Please point out the difference between rpm and tangential speed.

Yes. do that please. Give an answer. The question is what happens according to Newton's laws?I get a lot of good advice as to what I need to do. What happens when two perfect bodies collide? If you know, share it, for the sake of whatever deity you hold dear.

The blue ball will continue to move in the x direction at 4 m/s.

doubling the mass of the sun would not affect the orbital speed of the earth?

If you apply the same iterations to my original diagram you obtain the same result as shown in Newton's drawing. the blue ball maintains its original speed.

An impulse changes the direction, it does not change the speed, not in Newton's derivation of centripetal force nor in my simple diagram.