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The problem question is: What is the angular velocity of the ladder about its centre when the angle, of the ladder against the wall, is @=15 degrees ?

BUT, if the ladder length is L, then x² + y² = L² and differentiating this expression wrt time gives,[tex]2x\dot x + 2y\dot y = 2L \dot L = 0[/tex]

Therefore, [tex]x\cdot\dot x = -y\cdot\dot y[/tex]

However, if we are given [tex]\dot x =\dot y[/tex] (numerically), then this means that x = y!

But if x = y, then the ladder must be at an angle of 45 degrees, yes?

So, this means that the ladder has only one orientation, @ = 45 degrees, such that the speeds of the ends of the ladder are the same.

Is this right? Or have I made a mistake in my earlier working ?