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Constrained Motion : Intuitive Approach

In the given ...

Question

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

A

2 v cos θ

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B

\frac{v}{cos θ}

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C

\frac{v}{2 cos θ}

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D

\frac{2 v}{cos θ}

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Solution

The correct option is B $\frac{v}{cos θ}$
$l^{2} = x^{2} + y^{2}$
Differentiating with respect to t,
$2 l \frac{d l}{d t} = 0 + 2 y \frac{d y}{d t}$ ( $∵ x$ is constant its derivative is zero)
$\frac{d y}{d t} = \frac{d l / d t}{y / l} = \frac{v}{cos θ}$

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