Consider the problem of a $2-$D truss as shown in the figure above. The truss is pinned at one end and a roller support is applied at the other end. Note that the roller support

prevents motion in the x direction. A vertical concentrated force P is applied at the right end of the truss.

Model the problem with one $2-$node $($planar$)$ truss element. The nodeal coordinates are given as

x$1,$Y$1=(0,0)$

x$2,$Y$2=(1,2)$

$($a$)$ Determine the vertical displacement of node $2.$ Take E$=200$GPa,P$=1000$N and A$=10$mm$^(2).$

$($b$)$ Determine the axial stress $\backslash$sigma in the element.