$2-15)$ A control linkage for an airplane consists of a $800$ mm long rigid vertical member $CB$ that is supported by a pin at $C$ and a cable $AB.$ When no force is applied on the linkage, the cable $AB$ is unstretched and $CB$ is vertical. When a horizontal force of $P$ is applied to end $B,$ it moves point $B$ to $B^{\text{'}}$ and results in an average normal strain of ${}_{AB}=0\mathrm{.}004m\frac{m}{m}m$ in the cable $AB.$ Determine the horizontal displacement of point $B.$

Note: $CB$ is 'rigid' $-$ this implies that $CB$ does not deform and hence $CB\text{'}=CB=800$ mm