Answer
$W=544.6J$
Work Step by Step
Tension force provides the centripetal force here.
Before the guideline is pulled in, we have $T_i=\frac{mv_i^2}{r_i}$
After the guideline is pulled in, we have $T_f=\frac{mv_f^2}{r_f}$
From the information given, $T_f=4T_i$, so $$\frac{mv_f^2}{r_f}=\frac{4mv_i^2}{r_i}$$ $$\frac{v_f^2}{r_f}=\frac{4v_i^2}{r_i}$$ $$v_f=\sqrt{\frac{4r_fv_i^2}{r_i}}$$
We have $v_i=22m/s$, $r_i=16m$ and $r_f=14m$ $$v_f=41.16m/s$$
From the work-energy theorem, $$W=\frac{1}{2}m(v_f^2-v_i^2)$$
We know $m=0.9kg$, so $$W=544.6J$$
