A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is:  

(Given, initial temperature of the bullet = 127°C,

Melting point of the bullet = 327°C,

Latent heat of fusion of lead = 2.5 * 10⁴ J kg^-1,

Specific heat capacity of lead = 125 J/kg K)

40% of K.E. = $mc\Delta T+mL$  

$0.4*\frac{1}{2}*m{v}^2=m\left[125\left(327-127\right)+2.5*10^4\right]$                

$\Rightarrow 0.2v^2=\left[250*10^2+25*10^3\right]$                

$v^2=\frac{2*25*10^3}{0.2}$                

v = 5 * 100

v = 500 m/sec