# Thermodynamics, bullet fired into ice

I'm beginning to study basic thermodynamics and I want to solve this exercise:

It fires a lead bullet from $3g$ to $30^oC$ with a speed of $240\frac{m}{s}$ to a block of ice at $0^0C$. How much ice melts? (the bullet remains embedded in the ice).

I think that the energy becomes kinetic friction: $$Q=K=\frac{1}{2}mv^2=86,4J$$ Then, I can find the mass of ice from the ecuation of latent heat: $$Q=mL_{f}$$ $$\implies m= 0,26 g$$

Is this correct? Do not influence the temperature of the bullet?