Question

If A block is dragged on a smooth horizontal plane with the help of a light rope which moves with a velocity $v$ as given in the figure. Then find The horizontal velocity of the block .

• A. $v$
• B. $vsin\theta$
• C. $\frac{v}{sin\theta }$
• D. $\frac{v}{cos\theta }$

Answer 1

Answer: (C)

From geometry $l^2=x^2+y^2$ but $y$ is constant, hence differentiating, we have, $2l\frac{dl}{dt}=2x\frac{dx}{dt}$
But $\frac{dl}{dt}=v$ . Hence horizontal velocity of block,
$v_x=\frac{dx}{dt}$

$\Rightarrow lv=x.v_x$ or $v_x=\frac{l.v}{x}=\frac{v}{sin\theta }$