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Question

Consider a rod of length of $$l$$ resting on a wall and the floor. Its lower end pulled towards left with a constant velocity $$V$$. As a result the end $$B$$ starts moving down along the wall. Let us find the velocity of the end $$B$$ downward when the rod makes an angle $$\theta$$ with the horizontal.

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Solution

 Here the distance between the points is always same, thus the point must velocity components in the direction of line joining them i.e, along the length of the rod. If point $$B$$ is moving downwards velocity $${V}_{B}$$. Its component along the length of $${V}_{B} \sin {\theta}$$. Similarly velocity component of $$A$$ along the length of rod is $${V}_{A} \cos {\theta}$$. 
Thus we have:
$${V}_{B} \sin {\theta}={V}_{A} \cos {\theta}$$
$${V}_{B}=V \cos {\theta}$$

Physics

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