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  4. An iron rocket fragment initially at -100° C enters the earth's atmosphere almost horizontally and quickly fuses completely in atmospheric friction. Specific heat of iron is 0.11 kcal / kg ° C its melting point is 1535° C and the latent heat of fusion is 3 kcals / kg. The minimum velocity with which the fragment must have entered the atmosphere is

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Q. An iron rocket fragment initially at $-100^{\circ} C$ enters the earth's atmosphere almost horizontally and quickly fuses completely in atmospheric friction. Specific heat of iron is $0.11 \,kcal / kg ^{\circ} C$ its melting point is $1535^{\circ} C$ and the latent heat of fusion is $3 \,kcals / kg$. The minimum velocity with which the fragment must have entered the atmosphere is

Thermal Properties of Matter

Solution:

The entire kinetic energy of the fragment is changed to heat. Expressing mass $m$ in kilograms everywhere, we have
$ \frac{1}{2} m v^{2}=\left[m(30)+m(0.11)\left(1535^{\circ}+100^{\circ}\right)\right] 4184 $
$ v^{2}=(8368)[30+180] \simeq 1.76 \times 10^{6} $
$ \Rightarrow v=(\sqrt{1.76}) \times 10^{3}=1.32 \,km / s$