First slide

Connected bodies

Question

A block is dragged on a smooth plane with the help of a rope which moves with a velocity as shown in figure. The horizontal velocity of the block is

Moderate

A

$v$
B

$\frac{v}{\sin θ}$
C

$vsin θ$
D

$\frac{v}{\cos θ}$

Solution

$L^{2} = x^{2} + y^{2} ∴ y = constant$
$2 L \frac{dL}{dt} = 2 x \frac{dx}{dt} \Rightarrow \frac{dx}{dt} = \frac{L}{x} V Horizontal velocity v_{x} = \frac{v}{\sin θ} \frac{x}{L} = \sin θ or v_{x} - \frac{v}{\sin θ}$

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