# Four Ball Collision

Classical Mechanics Level 5

Four equal radii balls of masses 1kg, 2kg, 3kg, and 4kg as shown, each moving with velocity $$1 \text{ m/sec}$$ towards the same point $$P$$, collide at exactly the same instant. The points of contact form vertices of a square, the center of which is point $$P$$. When the balls fly apart after the collision, they move at velocities $$v_1, v_2, v_3, v_4$$.

If $${v_1}^{2}+{v_2}^{2}+{v_3}^{2}+{v_4}^{2}$$ can be expressed as $$\dfrac{A}{B}$$, where $$A,B$$ are coprime positive integers, then what is $$A+B$$?

Assume collisions are ideal, i.e., perfectly elastic and frictionless.

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