Question

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

Answer 1

$x^2+y^2=l^2$

Differentiating both sides w.r.t time-

$2x\frac{dx}{dt}+2y\frac{dy}{dt}=0$

$⟹\frac{dx}{dt}=-\frac{y}{x}\frac{dy}{dt}$

$⟹v=u\tan \theta$