$1.[30$ Pts$.]$ A $50-$foot$-$long, $1080-$lb gin pole used to raise sections of a communication tower is suspended by a standard steel cable of $\backslash (0\mathrm{.}110-\backslash$mathrm$\{$in$\}.^\{2\}\backslash )$ cross section with an effective modulus of elasticity of $\backslash (15\backslash$times $10^\{6\}\backslash$mathrm$\{$psi$\}\backslash ).$ As the gin pole descends at a constant speed of $50\backslash (\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$min$\}\backslash ),$ an accident causes the top of the cable, $100$ ft above the gin pole, to stop suddenly. From the impact factor, estimate the maximum elongation and maximum tensile stress developed in the cable. $[$Note: The gin pole shown in use below right is only for context$]$