Two particles A and B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown here. The velocity of A to the left is 10 m/s. What is the velocity of B when angle $α$ = 60^o ?

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9.8 m/s

5.8m/s

17.3m/s

10 m/s

answer is C.

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Detailed Solution

l² = x² + y²

differentiating both sides,
$2 x \frac{dx}{dt} + 2 y \frac{dy}{dt} = 0$ ( $∵$ l is a constant)
$2 {xϑ}_{x} = 2 {yϑ}_{y}$

$\begin{array}{l} ϑ_{y} = \frac{x}{y} ϑ_{x} = \tan 60 \times ϑ_{x} (∵ \frac{x}{y} = \frac{1}{\tan α} = \cot α) \\ = \frac{1}{\sqrt{3}} ϑ_{x} = \frac{1}{\sqrt{3}} \times 10 = 5.8 m / s \end{array}$

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