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, $2l\frac{d l}{d t}=2x\frac{d x}{d t}$
But $\frac{d l}{d t}=v$ . Hence horizontal velocity of block,
$v_{x}=\frac{d x}{d t}$

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