A block is dragged on a smooth plane with the help of a rope which with a velocity v as shown in fig. The horizontal velocity of the block is

See fig. The angle 0 and lengths l vary with time.Let at any instant, the length AB be /. Thenx2+y2=l2 or 2xdxdt+2ydydt=2ldldtThere is no vertical motion of the block. So,dydt=0,dxdt=Vx and dldt=V∴2xVx=2lv or vx=lxvor vx=v(x/l)=Vsin⁡θ.