Newton Law's of motion question

[Saitama]

Homework Statement

The velocity of end 'A' of rigid rod placed between two smooth vertical walls moves with velocity 'u' along vertical direction. Find out the velocity of end 'B' of that rod, rod always remains in contact with the vertical walls.

Homework Equations

The Attempt at a Solution

I have no idea where to start from.
Should i take the component of 'u' along the rod? But if so, then why should i do it?

 

[rl.bhat]

At any instant, if x and y are the distances of B and A from the bottom of the wall, and L is the length of the rod AB, then what is the relation between x , y and L?

 

[Saitama]

At any instant, if x and y are the distances of B and A from the bottom of the wall, and L is the length of the rod AB, then what is the relation between x , y and L?

Thanks for the reply rl.bhat!

$$L=\sqrt{x^2+y^2}$$
But how this relation would help me solve the problem?

 

[emailanmol]

Rl.Bhat has suggested a really good method.

Another method is that the relative velocity of the two ends along the rod should be 0.
This is because if there was relative velocity along the rod between the ends , then the rod would compress/elongate.
But we know the rod is rigid.So rel velocity should be 0.

 

[emailanmol]

Using rl. Bhats method as u said L^2 = x^2+ y^2

Differentiate the equation.
What is dl/dt, dx/dt and dy/dt

 

[Saitama]

Using rl. Bhats method as u said L^2 = x^2+ y^2

Differentiate the equation.
What is dl/dt, dx/dt and dy/dt

If i differentiate the equation.
dl/dt is zero because there is no change in the length of rod as the time passes.
dx/dt is the horizontal velocity of point B.
dy/dt is 'u'.

Thanks for the help, i have understood how to solve this problem.