Motion in Straight Line

Question

Two particles A and B are connected by a rigid rod AB as shown in figure. The rod slides along perpendicular rails. Where the rod subtends an angle a = 30° with the horizontal, the velocity of A is 10m/s. Find the velocity of B.

Solution

From figure given, we have
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Differentiating both sides w.r.t. t, we get
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$rightwards double arrow$ 2xu + 2yv = 0
$rightwards double arrow$ $space space space straight v equals negative straight x over straight y straight u equals negative straight u space cot space straight alpha$
Here,
Initial velocity, u = 10m/s
$alpha space equals space 30 degree$
$therefore space space space straight v space equals space minus left parenthesis 10 right parenthesis space c o t space 30 degree space space space space space space space space space space equals space minus 10 square root of 3 space straight m divided by straight s comma space is space the space velocity space of space straight B.$

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