Hmm, Let us think the problem in different way We till the probelm regarding the center of mass. We know that the length of the strip is l. The insect is at one end therefore the center of mass is at LM/2(M+m). Now the insect moves forward to the other end. The strip moves backward in accordance to maintain the same position of the center of mass. Now suppose d is the distance that the center of mass moves LM/2 (M+m)= (L/2-d)M +( L-d) m/(M+m) LM/2 = (L/2-d)M + (L-d)m now d is less than the length of the strip you have to study the above equation,Now this strip is moving at a velocity v_1. So now we have the time taken t_1 = d/(v_1) when the insect flies off vetically still the momentum is conserved and it continues to move with a velcocity v_1 in t_2 so now the rod moves L t_2 = L/v_1 so t2>t1 why optiond is not correct?/ well if you have the strip to have a much smaller mass than the insect then we have the velccity of the strip to be so great that the strip is no longer in contact with the insect and this is not the condition of the problem
----Hope This Helps ----Stuart Anderson ---Stuartanderson_cal@yahoo.com