Discussion and hints:
Consider an FBD of P – do any of the forces in the plane of motion for P create a moment about O?
Step 1: FBDs
Draw an FBD of P.
Step 2: Kinetics (angular impulse/momentum)
Write down the angular momentum expression for P about O: HO = m rA/O x vA. Looking at your FBD, is angular momentum about O conserved? Note that you are asked to find the velocity of P – this velocity vector has two components. From where do you get the second equation? Consider the work-energy equation.
Step 3: Kinematics
Consider using the polar coordinates description of velocity. You will need this in order to link together the angular impulse-momentum and work-energy equations of Step 2.
Step 4: Solve
Use your results from Steps 3 and 4 to solve for the two components of velocity for P.
Any questions?