The three blocks shown move with constant velocities. Find the velocity of block B. Given${\mathrm{v}}_{{\mathrm{p}}_2}=10\mathrm{m}/\mathrm{s}\downarrow ,{\mathrm{V}}_{\mathrm{c}}=2\mathrm{m}/\mathrm{s}\uparrow .\left(\text{ in }{\mathrm{ms}}^{-1}\right)$

The velocities of A &  P₂ are equal and opposite with respect to ground, while the velocities of B & C are equal and opposite with respect to P₂ . Consider upward as positive & downward as negative, so
$\begin{array}{l}\overline{{\mathrm{v}}_{\mathrm{A}}}=-\overline{{\mathrm{v}}_{{\mathrm{P}}_2}}\Rightarrow {\mathrm{v}}_{\mathrm{A}}=-(-10)=10\mathrm{m}/\mathrm{s}\uparrow \\ \overline{{\mathrm{v}}_{\mathrm{B},{\mathrm{P}}_2}}=-{\overline{\mathrm{v}}}_{\mathrm{C}.{\mathrm{P}}_2}\Rightarrow {\overline{\mathrm{v}}}_{\mathrm{B}.}-{\overline{\mathrm{v}}}_{{\mathrm{P}}_2}=-\left[{\overline{\mathrm{v}}}_{\mathrm{C}}-{\overline{\mathrm{v}}}_{{\mathrm{P}}_2}\right]\\ \Rightarrow \overline{{\mathrm{V}}_{\mathrm{B}}}-(-10)=-[2-(-10\left)\right]\Rightarrow \overline{{\mathrm{V}}_{\mathrm{B}}}=-22\mathrm{m}/\mathrm{s}\\ \text{ So }{\mathrm{v}}_{\mathrm{B}}=22\mathrm{m}/\mathrm{s}\downarrow \end{array}$