P$2\mathrm{.}22$ WP For the assembly shown in Figure P$2\mathrm{.}22,$ high$-$density polyethylene bars $(1)$ and $(2)$ each have coefficients of thermal expansion of $=88\frac{{10}^{-6}}{}F.$ If the temperature of the assembly is decreased by $50F$ from its initial temperature, determine the resulting displacement of pin $B.$ Assume that $b=32$ in$.$ and $=55.$