# Confusing Collisions

$$N$$ spheres are placed in a semicircle on a frictionless surface. The mass of all these spheres is $$m_1$$.

A sphere of mass $$m_2$$ is then projected so that it collides with all $$N$$ balls and finally leaves the semicircle, moving towards the right.

If $$N\to \infty$$, the ratio between the final and initial velocities of $$m_2$$ is $-\frac{a}{b}$

Find $$a+b$$.

• You might wish to make small approximations.

• This is part of Ordered Disorder.

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