Final answer:
When the man on the ladder climbs upward, the balloon moves downward at the same speed as the man. If the man stops climbing, the speed of the balloon will be lower than the speed at which the man was climbing.
Step-by-step explanation:
(a) In what direction and (b) at what speed does the balloon move?
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the man on the ladder climbs upward, he exerts a force on the ladder and the ladder exerts an equal and opposite force on him. This force also acts on the balloon, causing it to move in the opposite direction of the man. Therefore, the balloon moves downward.
To find the speed of the balloon, we can use the principle of conservation of momentum. Before the man starts climbing, the total momentum of the system (man + ladder + balloon) is zero, since they are initially stationary. When the man starts climbing, he gains momentum in the upward direction. To conserve momentum, the balloon must gain an equal amount of momentum in the downward direction. Therefore, the speed of the balloon is equal to the speed at which the man is climbing, which is 2.5 m/s relative to the ground.
(c) If the man then stops climbing, what is the speed of the balloon?
If the man stops climbing, his momentum becomes zero, as he is now at rest relative to the ladder. To conserve momentum, the balloon must have a momentum in the downward direction equal to the momentum the man had before stopping. Since momentum is mass multiplied by velocity and the mass of the balloon is greater than the mass of the man, the speed of the balloon will be lower than the speed at which the man was climbing. However, without information about the specific masses of the man and the balloon, we cannot calculate the exact speed of the balloon when the man stops climbing.