# Frictionless Slide Propulsion

The part of mass $$m$$ in the figure above slides down the frictionless surface through height $$h$$ and collides with the uniform vertical rod of mass $$M$$ and length $$d$$, sticking to it. The rod pivots about the point $$o$$ through the angle $$\theta$$ before momentarily stopping. Then $$\theta$$ can be expressed as

$\theta = \cos^{-1} \left[ \alpha - \frac{ \beta m^2 h } { d ( \gamma m +M) \times ( \nu m + M ) } \right]$

What is the value of$$\alpha+\beta+\gamma+\nu$$?

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