Finding Angular and Linear Velocity in a Sliding Bar System

[mpn17]

Homework Statement

The ends of the slender bar remain in contact with their respective support surfaces. If end has a velocity in the direction shown, determine the angular velocity of the bar and the velocity of end.

Answers:
ω=1.394 rad/s V_A=0.408 m/s down

Homework Equations

Va=Vb +Va/b
law of sines
V=rw

The Attempt at a Solution

I've tried using the angles given to use the law of sines and the velocity given into find Va/b or Va and then using V=rω to find the angular velocity but have had no luck. Any help would be appreciated

 

[CWatters]

Hint: Each end of the rod has a component of it's velocity in the direction of the rod. These components must be the same or the length of the rod would change.