Question

Two rods are moving with constant velocity $v=10m/s$ in perpendicular direction to their length as shown in figure. The velocity of point of intersection of two rods (in m/s) will be :

• A. $20$
• B. $10$
• C. $50$
• D. $5$

Answer 1

The correct option is A $20$

Consider the given simplified diagram.
$\frac{dx}{dt}=vsin\theta -v^{\prime }$

$\frac{dy}{dt}=-vcos\theta$

$y=xtan\theta$ (always)

As $\theta$ is not changing with time we get
$\frac{dy}{dt}=\frac{dx}{dt}tan\theta$

$-vcos\theta =(vsin\theta -v^{\prime })tan\theta$
$v^{\prime }tan\theta =\frac{vsi{n}^2\theta }{cos\theta }+vcos\theta$
$v^{\prime }=\frac{v}{cos\theta \times \frac{sin\theta }{cos\theta }}$

$\therefore v^{\prime }=vcosec\theta =10\times 2=20m/s$

$(\theta ={30}^o$ and $cosec{30}^o=2)$