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

Let at any instant of time, the length AB be l, here angle θ and length l vary with time, then using Pythagoras theorem in ∆ABC,x2 + y2 = t2On differentiating both sides w.r.t t, we getor  2xdxdt+2ydydt=2ldldtAs, there is no vertical motion of the block, sodydt=0,dxdt=vx and   dldt=v∴  2xvx = 2lv or   vx=lxv   or   vx=vxl=vsinθ