A lead bullet penetrates into a solid object and melts. Assuming that 50% of its kinetic energy was used to heat it, calculate the initial speed of the bullet. The initial temperature of the bullet is `27^@C` and its melting point is `327^@C`. Latent heat of fusion of lead `= 2.5 xx 10^4 J//kg` and specific heat capacity of lead `=125 J//kg.K`.

Explanation

Let the speed of bullet be `v`. The `50%` of kinetic energy is used in increasing the temperature from `27^@C` to `327^@C` and them melting the bullet.
`(1)/(2).(1)/(2)mv^2=msDeltatheta+mL_("fusion")`
`(v^2)/(4)=125xx(327-27)+2.5xx10^4`
`=3.75xx10^4+2.5xx10^4`
`v^2=4xx6.25xx10^4`
`v=2xx2.5xx10^2=500 m//s`