$1.(40$ marks$)$ A bomb $($JDAM$)$ is released at $\backslash ($ t$=0\backslash )$ with an initial velocity along the horizontal direction, $\backslash ($ v b$=200\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ A anti$-$aircraft system $($LD$-2000)$ fires immediately to intercept the bomb. The projectiles $($from the gun$)$ have an initial speed $($muzzle velocity$)$ of $\backslash ($ v$\_\{$a$\}=1,000\backslash )\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The distance between the bomb and the anti$-$aircraft gun is shown in the graph. Neglect aerodynamic effects.

$(1)$ Determine the angle $\backslash (\backslash$theta $\backslash )$ for the projectiles that allows successful interception.

$(2)$ Identify the time $\backslash ($ t$^\{\backslash$prime$\}\backslash )$ and the height $\backslash ($ h $\backslash )$ at which the projectiles hit the bomb.

P$.$S$.$ This problem is designed solely for the practice of kinematics priciples and is never intended to promote violence or military conflict. Indeed, in the given scenario, nobody will be injured regardless of the involvement of weapons.