Problem #$5.[10$ pts$.]$ An unfocused laser beam impinges upon a semi$-$infinite metal workpiece, delivering a constant power $.$ The beam has area A $=$ a $$ a and is moving with velocity V$.$ In the metal exposed to the laser $(,0)=0$ and $(0,)=0$ and $($$,)=0,$ where q$0$ is the $($constant$,$ uniform$)$ heat flux. The solution is $(,)=0+20$$$ ierfc $(2$$).$ The highest temperature that the metal in the workpiece attains under this treatment is Tmax. Where does Tmax occur in relation to the beam? What is Tmax in terms of $?$ Assume perfect absorption of the radiation by the workpiece. Note that the integral complementary error function ierfc$($z$)$ is defined as ierfc$()=$ erfc$($$)$ $=1$ exp$(2)[1$ erf$()].$