Question

Figure shows two rods p & q moving with a same velocity of $2\text{m/s}$ perpendicular to their length. If angle between the rods is ${106}^{\circ }$, velocity of point of intersection (in$\text{m/s}$) is.

Answer 1

Say, DB = CB = x
By triangle $ACB$,
$sin\theta =\frac{BC}{AB}$
$\Rightarrow AB=\frac{BC}{\sin \theta }$
By differentiating the equation on both sides,
$v_A=\frac{v}{\sin \theta }=\frac{2}{sin53}=\frac{2\times 5}{4}=2.5\text{m/s}$