Question

In the given figure find the velocity of the block $M$, if both the rope ends are pulled with a velocity $v$.

• A. $2v\cos \theta$
• B. $\frac{v}{\cos \theta }$
• C. $\frac{v}{2\cos \theta }$
• D. $\frac{2v}{\cos \theta }$

Answer 1

The correct option is B $\frac{v}{\cos \theta }$

$l^2=x^2+y^2$
Differentiating with respect to t,
$2l\frac{dl}{dt}=0+2y\frac{dy}{dt}$ ($\because x$ is constant its derivative is zero)
$\frac{dy}{dt}=\frac{dl/dt}{y/l}=\frac{v}{\cos \theta }$