The angular momentum is defined as,
Acording to this text we know for conservation of angular momentum that
Where is initial momentum
is the final momentum
How there is a difference between the stick mass and the bug mass, we define that
Mass of the bug= m
Mass of the stick=10m
At the point 0 we have that,
Where l is the lenght of the stick which is also the perpendicular distance of the bug's velocity
vector from the point of reference (O), and ve is the velocity
At the end with the collition we have
Substituting
Applying conservative energy equation we have
Replacing the values and solving
Substituting
l=\frac{13}{0.54(9.8)}