6. (10 points) A snowball with a temperature of $0^{\circ} \mathrm{C}$ is launched at a speed of $v$ towards a wall. Upon impact, $k=0.02\%$ of the snowball melts. Determine what percentage of the snowball will melt if it is launched towards the wall at a speed of $\frac{v}{2}$? The specific latent heat of fusion of snow is $\lambda=330$ kJ/kg. Assume that all the energy released upon impact goes into melting the snow.
Answer: $n=0.005\%$

Solution. The law of conservation of energy in the first case: $\frac{m v^{2}}{2}=\lambda \frac{k m}{100}$. (3 points)

That is, the speed of the snowball: $v=\sqrt{\frac{\lambda k}{50}}=\sqrt{132} \mathrm{M} / \mathrm{c}$.

In the second case: $\frac{m\left(\frac{v}{2}\right)^{2}}{2}=\lambda \frac{n m}{100}$.

Finally, we get: $n=0.005\%$.