I have a ladder which is propped up against a wall. The ladder slides down the wall and is constrained to move such that the speeeds of the ends of the ladder against the wall (and floor) are a constant value. i.e. [tex]\dot x = \dot y = constant[/tex] 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 ?