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An iron meteorite melts when it enters the Earth's atmosphere. If its initial temperature was \SI{125}{\degreeCelsius} outside of Earth's atmosphere, calculate the minimum velocity the meteorite must have had before it entered Earth's atmosphere. (Iron melts at \SI{1535}{\degreeCelsius}, its specific heat is \SI{450}{\joule\per\kilo\gram\per\kelvin} and its latent heat of fusion \SI{2.77e5}{\joule\per\kilo\gram}.) $\star$
$\SI{1.4}{\kilo\meter\per\second}$
If the iron meteorite melts, it must be heaten up to irons melting point ($\theta_f=\SI{1535}{\degreeCelsius}$) and then be melted. The energy for these two processes comes from the meteorites speed, hence: \begin{align} \Ekin &= Q\\ \Ekin &= Q_{\Delta} + Q_f\\ \frac12 mv^2 &= c \cdot m \cdot\Delta\theta + m\cdot L_f\\ \frac12 v^2 &= c \cdot\Delta\theta + L_f\\ v &= \sqrt{2c\Delta\theta + 2L_f}\\ &= \SI{1400}{\meter\per\second} \end{align}
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