# A Problem from my book 6

**Classical Mechanics**Level 3

In cold regions, the temperature of the surrounding is \(-20^\circ C\). The water of the lake starts freezing and freeze up to a maximum depth.Find the maximum depth of ice sheet in meters formed. If the height of lake before freezing was \(19 \text{ m}\).

You are given that:

\( \dfrac{\rho_{\text{ice}} }{\rho_{\text{water}}} = 0.9 \).

\( \dfrac{K_{\text{water}} }{K_{\text{ice}}} = 5 \).

Maximum density of water is at \(4^\circ C\).

Where \(K\) is the thermal conductivity of substance.