Problem data: S2 (length of the second section of the icicle path) = 20 m; t2 (considered fall time) = 1 s.
Constants: g (acceleration due to gravity) ≈ 10 m / s2.
1) The speed of the icicle before the second section of the path: S2 = V * t2 + g * t2 ^ 2/2, whence we express: V = (S2 – g * t2 ^ 2/2) / t2 = (20 – 10 * 1 ^ 2 / 2) / 1 = 15 m / s.
2) The length of the first part of the icicle path: S1 = V ^ 2 / 2g = 15 ^ 2 / (2 * 10) = 11.25 m.
3) Roof height: S = S1 + S2 = 11.25 + 20 = 31.25 m.
Answer: The roof height is 31.25 m.
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