## Essential University Physics: Volume 1 (4th Edition)

$L_0=\frac{5}{7}L_f$
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: $(\frac{3v}{v})^2(L_f-L_0)=2(2L_f-L_0)$ $(\frac{9}{1})(L_f-L_0)=2(2L_f-L_0)$ $L_0=\frac{5}{7}L_f$