According to kinetic energy theorem:
FL= 12mBv2B
Get: VB = 2flmb
After that, A and B move at the same speed, which is obtained by the conservation of momentum:
mBvB=(mA+mB)vAB
After that, AB accelerates uniformly, which can be obtained from Newton's second law and kinematics formula:
v′2AB-v2AB = 2ax，
a=FmA+mB
X = 0.75- 1, VAB'= 23/s.
Simultaneous solution: l = 0.25m
Answer: The length L of the rope connecting two objects is 0.25 meters.