A $3\mathrm{.}74-$ton elevator is supported by a standard steel cable of $2\mathrm{.}3-$in$\mathrm{.}2$ cross section and an effective modulus of elasticity of $12*106$ psi. As the elevator is descending at a constant $336$ ft$/$min$,$ an accident causes the top of the cable, $51\mathrm{.}22$ ft above the elevator, to stop suddenly. Estimate the maximum elongation $($deflection$)$ developed in the cable $($see the figure below$).$ Submit your answer in inches.