[Momentus (OP)]

I'm sorry that you can't work out this problem.  But since you don't know how to do the math it doesn't make much sense for you to claim you can guess the answer.

The direction that the blue mass is now moving can be determined by simple geometry. It is moving along the hypotenuse of a right-angled triangle at 4 units and along the perpendicular side of the triangle at 3 units. Just as drawn in the original diagram.

[Momentus (OP)]

Sir Isaac Newton formulated his 3 laws some 350 years ago. He the used these laws to establish the theoretical motion of a mass when subjected to a perpendicular force.
I copied the diagram he used to show what happens when a body is subjected to a perpendicular force.

In this drawing he represents the direction of the mass by a drawn line, and the speed of the mass by the length of the line. His drawing shows that the length of the line is not changed by the applied impulse.
In the drawing he repeats the action, changing the direction of the line, but not the length of the line.
He does this repeatedly with the same result, perpendicular force, change of direction, constant speed.

Form this he goes on to derive centripetal force and his theory of gravity.

My diagram shows exactly the same thing as Newton?s 350 year old drawing.
Perpendicular force changes the direction of a moving mass. It does not change the speed.

[Origin]

My diagram shows exactly the same thing as Newton?s 350 year old drawing.
Perpendicular force changes the direction of a moving mass. It does not change the speed

A collision is not an example of centripetal force. 
In Newtons model of orbital motion there is a continuous force that is perpendicular to the direction of an objects motion.  In a perfectly circular orbit the objects speed would be constant, only the direction would change.  That is not what we are talking about here.  There is no continuous force, you are trying to apply centripetal force to a situation where it doesn't apply.

[Bored chemist]

The diagram shows a blue ball traveling at a velocity of A-C, which is struck by a red ball traveling at a velocity of B-C.
The Blue ball is deflected with a resultant velocity C-D, the vector change is solely of direction, the red ball comes to rest its vector change is solely of magnitude.

What happens to the kinetic energy of the red ball?

[Momentus (OP)]

speed would b constant, only the direction would change

Finally some understanding of perpendicular force.
In the principia Newton uses impulses, to establish centripetal force, only moving on to continuous force at the end

[Momentus (OP)]

What happens to the kinetic energy of the red ball?

I think that is an excellent observation. Do you recall the title of the thread?
Kinetic energy only seems to have a value within a particular frame of reference, as you point out.
There is a relationship between speed and mass (E=mc2) which must apply to the red ball, even though the change must be infinitesimally small. The asymmetrical nature of dark motion raises many such queries.

[Bored chemist]

I think that is an excellent observation

It wasn't an observation, it was a question.
And it's a question which you failed to answer.

[Origin]

Finally some understanding of perpendicular force.

I think everyone here understands centripetal force and they also know that centripetal forces are different than a collision of 2 masses, which is something that you don't understand.

[Origin]

The asymmetrical nature of dark motion raises many such queries.

I think you have clearly proven that your idea of dark motion is just your misunderstanding of basic Newtonian mechanics.

[Momentus (OP)]

I think everyone here understands centripetal force and they also know that centripetal forces are different than a collision of 2 masses, which is something that you don't understand.

The collision of two masses provides a force, which arises from the deceleration of the red ball. Newton, in the passage from the Principia which I have quoted, uses an impulse to change the direction of a mass. He then uses calculus to extend the proven case of a single impulse into a continuous force.
He shows that a perpendicular impulse changes the direction of a mass and does not change the speed, just as the diagram I have posted.
It is of no consequence that in your opinion the popular vote supports your argument. Science depends upon facts not belief.

[Bored chemist]

Science depends upon facts not belief.

The facts of dark matter and dark energy are established.
Your belief that they have anything to do with your diagram is irrelevant.

I'm curious.
What do you think the phrases "dark matter" and "dark energy" mean?

[Momentus (OP)]

The anomalous motion of the distant galaxies. Their motion does not fit with the existing Laws. Mysterious and unseen forces are at work. No consensus on what dark energy is, nobody has found dark matter.

[Origin]

He shows that a perpendicular impulse changes the direction of a mass and does not change the speed, just as the diagram I have posted.

No, your chart clearly shows that the speed increases.
Before the collision the blue ball is moving at 4 units of speed along the x direction and 0 units in the y direction so the overall speed is 4 units.
After the collision the blue ball is moving 4 units in the x direction and 3 units in the y direction so the overall speed of the blue ball is 5 units.

You have shown in your diagram that the speed increases.

The only conclusion I can come up with is either you simply unable to understand basic math and basic Newtonian mechanics or you are a troll. 
If it is simple ignorance, it is too bad you refuse to accept any help to clear up your understanding.

[Momentus (OP)]

No, your chart clearly shows that the speed increases.

Newton's "chart" shows that the speed does not increase. My chart is the same as Newton's "chart".
Why do you refuse to acknowledge this.?

[paul cotter]

I give up at this point. Your errors and misinterpretations have been more than adequately addressed yet you cannot or will not see sense.

[Bored chemist]

My chart is the same as Newton's "chart".

No, it's not.
The string holding a ball to a circular path does no work.
A ball colliding with something  and stopping does do work.

Why do you refuse to acknowledge this.?

Because it's wrong.

[Origin]

Newton's "chart" shows that the speed does not increase.

Newtonian mechanics says the speed increases.

My chart is the same as Newton's "chart".

Your chart shows that the speed increases.  It is right there in your math and you show that the speed is 5 units.  The fact that you show the speed increases and then state that the speed doesn't increase is rather insane.

Why do you refuse to acknowledge this.?

Because I'm not insane.

This is pointless!  Normally I would do the math to show you that you are incorrect and the speed increases except you have already done that and proven that you are wrong.
Absolutely bizarre. 

[paul cotter]

Origin, you are correct,  it's utterly pointless. The relevant errors have been pointed out repeatedly and the only conclusions are ( 1) an inability to understand, or ( 2 ) a dogged determination not to understand.

[Momentus (OP)]

n Newtons model of orbital motion there is a continuous force that is perpendicular to the direction of an objects motion.  In a perfectly circular orbit the objects speed would be constant, only the direction would change.  That is not what we are talking about here.  There is no continuous force, you are trying to apply centripetal force to a situation where it doesn't apply.

Isaac NEWTON: Philosophiae Naturalis Principia Mathematica. 3rd Ed.
Book I Section II.
Translated and Annotated by Ian Bruce. Page 95
SECTION II. On the finding of centripetal forces.
PROPOSITION I. THEOREM I.

Truly, when the body comes to B, by a single but large impulse the centripetal force acts, and brings about that the body deflects from the line Bc and goes along in the line BC ; cC is acting parallel to BS itself, crossing BC in C; and with the second part of the time completed, the body (by the corollary to Law I.) may be found at C


 Newton Centripetal.png (25.16 kB . 221x219 - viewed 31 times)

By a single but large impulse the centripetal force acts
Those are Newton?s words,
Newtons model of orbital motion there is a large but single force that is perpendicular to the direction of an objects motion. The  objects speed would be constant, only the direction would change.

[Momentus (OP)]

You believe that a point located at x=4 units and y=3 units is 4 units from the origin

That would be the point on the drawing marked X. So yes I can do simple vectors.