Ball collides with a door and pushes it open

[TjGrinnell]

Homework Statement

A door has a mass of 9.00 kg, a height of 2.00 m, a width of 1.00 m, and a moment of inertia of 3.00 kg*m2 about its axis. It is initially at rest and partly open. A 2.00 kg ball is thrown at the door. When it hits the door it is 1.20 m above the floor and 0.450 m from the hinge axis. It is moving at 3.50 m/s perpendicular to the door's surface, and it bounces back, also perpendicular to the door's surface at 2.00 m/s.
What is the angular speed of the door after the collision
If the collision takes place over 0.05 s, what was the average force between the ball and the door?

Relevant Equations

KE[SUB]b1[/SUB]+PE[SUB]d[/SUB]=KE[SUB]b2[/SUB]+KE[SUB]d[/SUB]

F[SUB]avg[/SUB]=m(v[SUB]f[/SUB]-v[SUB]0[/SUB])/t
Have to type here because of picture. I think I may have done this wrong the first time and I wanted to know if i should use the conservation equation as shown above, or I the one in my work correct?
And also is the second formula the correct one in order to get the average force?
Thank you

 

[haruspex]

KE_b1+PE_d=KE_b2+KE_d

if i should use the conservation equation as shown above, or I the one in my work correct?

Never assume conservation of mechanical energy without good cause.
What other laws could you use?