Body connected to two parts of a rope on an inclined plane

[Like Tony Stark]

Homework Statement

The picture shows a mass $A$ falling with velocity $400 cm/s$ and acceleration $16 cm/s^2$.
The mass $B$ is connected to $A$ as depicted in the picture.

Relevant Equations

##V_{B/A}=V_B - V_A

The thing is that my professor said that if the velocity of $A$ is $400 cm/s$, the velocity of $B$ is $200 cm/s$ because "$B$ is connected to two parts of the rope and $A$ is conected just to one part", and he also said that that $200 cm/s$ is the velocity of $B$ with respect to $A$.
And I didn't understand any of them. Why is the velocity of $B$ half the velocity of $A$? (I don't understand what the "two parts of the rope" have to do with the velocity)
And why is that velocity the velocity of $B$ with respect to $A$?

 

[mitochan]

Hi.
It's a kind of pulley which is usually set vertical but here sloped. Pulley makes required pulling force half and pulling length double to lift up weight. The double-length relation holds here.

 

[Like Tony Stark]

Hi.
It's a kind of pulley which is usually set vertical but here sloped. Pulley makes required pulling force half and pulling length double to lift up weight. The double-length relation holds here.

Hi!
Oh, so that's because there are two pulleys??

And can you explain me why is that velocity with respect to $A$?
Thanks

 

[mitochan]

The pulley fixed to weight A plays a simple role of changing the direction of force. Another pulley, movable pulley plays the key role. Imagine if there were no movable pulley between, the weight B tied with rope coming from the fixed pulley would do more (double) displacement on the slope. Change of rope length after the fixed pulley is half consumed by the part between the movable pulley and joint of the rope and the slope.

The slope is fixed to A. The speed to the slope is the speed to A.

 

[haruspex]

Homework Statement: The picture shows a mass $A$ falling with velocity $400 cm/s$ and acceleration $16 cm/s^2$.
The mass $B$ is connected to $A$ as depicted in the picture.
Homework Equations: $V_{B/A}=V_B - V_A$

The thing is that my professor said that if the velocity of $A$ is $400 cm/s$, the velocity of $B$ is $200 cm/s$ because "$B$ is connected to two parts of the rope and $A$ is conected just to one part", and he also said that that $200 cm/s$ is the velocity of $B$ with respect to $A$.
And I didn't understand any of them. Why is the velocity of $B$ half the velocity of $A$? (I don't understand what the "two parts of the rope" have to do with the velocity)
And why is that velocity the velocity of $B$ with respect to $A$?

Consider A moving down a distance y. The length of string above A increases by y. The total length of string is constant, so the length that goes from A's pulley around B's pulley and back to A reduces by y.
If the reduction in length from A's pulley to B's pulley is x, by how much is the bit that goes back up to A reduced?