Conceptual Question, please help!?

Question

A balloon of mass M is floating motionless in
the air. A person of mass less than M is on
a rope ladder hanging from the balloon. The
person begins to climb the ladder at a uniform
speed v relative to the ground.
How does the balloon move relative to the
ground?
1. The balloon does not move.
2. Down with a speed less than v
3. Up with speed v
4. Down with speed v
5. Up with a speed less than v

Answer 1

The key here is that the center of gravity of the ballon/ladder/person system cannot move, because no external force has been applied. Or, expressing it in a way that makes it easier to solve the problem, the total momentum of the system must be zero. If the person has mass less than M and moves upwards at speed v, he or she has upwards momentum Mv. The balloon of mass M needs to move downwards at a speed less than v in order to achive downwards momentum Mv. So the answer is 2) down with a speed less than v.