Given a change in internal energy, how can I find the temperature

[mp0295]

Homework Statement

Two speeding lead bullets, one of mass 15.0 g moving to the right at 270 m/s and one of mass 7.65 g moving to the left at 390 m/s, collide head-on, and all the material sticks together. Both bullets are originally at temperature 30.0°C. Assume the change in kinetic energy of the system appears entirely as increased internal energy. We would like to determine the temperature and phase of the bullets after the collision. (Lead has a specific heat of 128 J/(kg K), a melting point of 327.3°C, and a latent heat of fusion of 2.45 104 J/kg.)

(e) What is the temperature of the combined bullets after the collision?

(f) What is the phase of the combined bullets after the collision?
m_bullet,solid= ____ g
m_{bullet,liquid}= ____ g

Homework Equations

I have already correctly found the change in internal energy to be 1098J.


Q=mc\DeltaT
Q=L\Deltam

The Attempt at a Solution

I really don't know how to do this.

I tried finding the heat required to raise the temperature from 30C to the melting point using Q=mc\DeltaT => Q=.0226kg*128J/(kgK)*297.3K and found this to be 860J but I don't know where to go from there.

 

[Simon Bridge]

Imagine this was ice instead - you start with ice at -30degC and you heat it ... the ice warms up to 0degC right? Then what?

Same with the bullets - so 860J out of the 1098J goes to warming the bullets until they are ready to melt.
How much energy goes into melting the bullets?