A 200-kg package is being hoisted by a \(120-\mathrm{mm}\)-diameter steel cable \(\left(E=200 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\right)\) at a constant velocity \(v\). What is the largest value of \(v\) such that the cable's elastic strength of \(560 \times 10^{6} \mathrm{~N} / \mathrm{m}^{2}\) is not exceeded if the hoisting mechanism suddenly fails when the cable has a length of \(10 \mathrm{~m}\).