A uniform, horizontal flagpole $5\mathrm{.}00$ m long with a weight of $200$ N is hinged to a vertical wall at one end. A $600-$N stuntwoman hangs from its other end. The flagpole is supported by a guy wire running from its outer end to a point on the wall directly above the pole. $($a$)$ If the tension in this wire is not to exceed $1000$ N$,$ what is the minimum height above the pole at which it may be fastened to the wall? $($b$)$ If the flagpole remains horizontal, by how many newtons would the tension be increased if the wire were fastened $0\mathrm{.}50$ m below this point?