For the truss in Fig. P$44,$ a horizontal load of $P=4000lb$ is applied in the $x$ direction at node $2.$

$($a$)$ Write down the element stiffness matrix $k$ for each element.

$($b$)$ Assemble the $K$ matrix.

$($c$)$ Using the elimination approach, solve for $Q.$

$($d$)$ Evaluate the stress in elements $2$ and $3.$

$($e$)$ Determine the reaction force at node $2$ in the $y$ direction.