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Home » Wait: perhaps Sₙ = 110 is approximate? - NBX Soluciones

Wait: perhaps Sₙ = 110 is approximate? - NBX Soluciones

📅 May 3, 2026 👤 scraface

May 03, 2026

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\( \frac{2}{5} h^{5/2} = -\frac{28.8}{25\pi} t + C \)
At \( t = 0 \), \( h = 12 \): \( C = \frac{2}{5} \cdot 12^{5/2} \appro...
At \( t = 10 \):
\( \frac{2}{5} h^{5/2} = 199.726 - \frac{28.8}{25\pi} \cdot 10 \)
\( \frac{28.8}{25\pi} \cdot 10 = \frac{288}{25\pi} \approx 3.648 \)
So \( \frac{2}{5} h^{5/2} = 199.726 - 3.648 = 196.078 \)
\( h^{5/2} = \frac{5}{2} \cdot 196.078 = 490.195 \)
Now \( h = (490.195)^{2/5} \)
\( \ln(490.195) \approx 6.192 \), \( \frac{2}{5} \times 6.192 = 2.477...
So \( h \approx 11.94 \) cm.

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