Max Angle Rod Rotates when Hit w/ Ball

[TerpFlacco]

EDIT: Title should say "To what maximum angle, measured from vertical, does the rod rotate when hit will a ball?" Did not see that it had cut off. Sorry.

Homework Statement

A 78 g, 40-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 14 g ball of clay traveling horizontally at 2.4 m/s hits and sticks to the very bottom tip of the rod.

To what maximum angle, measured from vertical, does the rod (with the attached ball of clay) rotate?

MR = .078kg
L=.4m
MB = .014kg
v= 2.4m/s

Homework Equations

p=mv
L=Iω
Erot = .5*I*ω²

The Attempt at a Solution

I start off by finding the momentum of the ball as MB*v = 0.0336 kg-m/s

Then, I find angular momentum as 0.01344 kg-m^2/s

Next, I use I = (MR/3 + MB)*L^2 to get I as 0.0064 kg-m^2

Using angular momentum equaling I*omega, I find omega as 2.1 rad/s.

To find rotational energy, I used .5*I*omega and got 0.014112J

And now I do not know what to do...

 

[Quinzio]

You can use angular speed, but you don't need to.
What you just need is to keep in mind that the kinetic energy of the ball will translate into potential energy, that is $$mgh=(mv^2)/2$$.
The rod does not contribute to this energy transfer as it's axle passes through its center.