Grain is loaded onto a train initially coasting at the speed \(v_0 \text{ m/s}\) by dropping it vertically from a stationary silo at the rate \(\alpha_m \text{ kg/s}\). How long does it take for the train to pass the silo (in seconds)?

**Details**

- The train is \(l = 200\) m long, and has an empty weight of \(m_0 = 500\) kg.
- \(v_0=45\) m/s
- \(\alpha_m = 20\) kg/s

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