Answer
$L_0=\frac{5}{7}L_f$
Work Step by Step
a) While there is a way to use complex math to arrive at the equation necessary to find this answer, we can also use proportions to obtain:
$(\frac{3v}{v})^2(L_f-L_0)=2(2L_f-L_0)$
$(\frac{9}{1})(L_f-L_0)=2(2L_f-L_0)$
$L_0=\frac{5}{7}L_f$
