A block is dragged on a smooth plane with the help of a rope which moves with velocity (v) shown in Fig. 2 (CF). 25 , The horizontal velocity of the block is .

A block is dragged on a smooth plane with the help of a rope which mov

1.	A block is dragged on a smooth plane with the help of a rope which moves with velocity (v) shown in Fig. 2 (CF). 25 , The horizontal velocity of the block is .
Answer» `v` ` v SIN THETA ` v//sin theta` `v//cos theta` Solution :LET ` AB = X, then ` AC= x cos theta` :. ` (d(AC)/(dt) = d/(dt) (x cos theta) = (DX)/(dt) cos theta + x (- sin theta) (d theta)/(dt)` But `(d(AC)/(dt) = 0 `, so ` 0= (dx)/(dt) cos theta + x ( - sin theta) ( d theat)/(dt)` or ` v cos theta = x sin theta = x sin theta (d theta)/(dt)` or ` (dtheta)/(dt) = ( v cos theta)/(x sin theta)` . Also , ` CB = x sin theta`. Velocity of block will be ` u = sin theta + x cos theta xx (v cos theta)/( x sin theta)` ` (v (sin^@ theta + cos^2 theta)/( sin theta) = v/(sin theta)`.