A $34-$foot$-$long, $852-$lb gin pole used to raise sections of a communication tower is suspended by a standard steel cable of $0\mathrm{.}110-$in$\mathrm{.}2$ cross section with an effective modulus of elasticity of $12*106$ psi. As the gin pole descends at a constant speed of $30$ ft$/$min$,$ an accident causes the top of the cable, $77$ ft above the gin pole, to stop suddenly. Estimate the maximum elongation developed in the cable. Submit your answer in inches.