How Fast Was the Bullet That Hit the Pendulum?

[candycooke]

A 12.5 g bullet is shot into a ballistic pendulum that has a mass of 2.37 kg. The pendulum rises a distance of 9.55 cm above its resting position. What was the speed of that bullet?
m(bullet) = 0.0125 kg
m(pendulum) = 2.37 kg
h = 0.0955 m

I know that I'm supposed to use conservation of energy:
P(i)=P(f)
m(1)v(i)=(m(1)+m(2))v(f)

Unfortunately this equation does not take into account how high the pendulum swung, which is obviously an important factor.

 

[Doc Al]

Treat this problem as having two parts:
(1) The collision of bullet and pendulum. (What's conserved here?)
(2) The swinging of pendulum+bullet after the collision. (What's conserved here?)