Angular Velocity: Formula for Max Velocity of Wood Block

[Brett bALL]

This is my first contact and please excuse my limited knowledge of physics.
see attached sketch.
If the steel plate is moved along the steel table in direction A at a given velocity, what is the formula for the angle to achieve maximum velocity of the wood block in direction B.

 

[chaoseverlasting]

Hi,

Im assuming that you have a basic knowledge of calculus.

If you assume that the plate moves in the direction A with a velocity v, then the block moves with a velocity $$vcos(\theta)$$ along the plank in the downward direction.

The projection of this velocity along the B and A direction is $$vcos\thetasin\theta$$ and $$vcos\thetacos\theta$$

$$V_B=vcos(\theta)sin(\theta)$$
Differentiate this expression wrt $$\theta$$ and equate to zero to get max value.

Otherwise, you can find the max value of Vb using trig.